text:
The median is de vawue separating de higher hawf from de wower hawf of a data sampwe (a popuwation or a probabiwity distribution). For a data set, it may be dought of as de "middwe" vawue. For exampwe, in de data set [1, 3, 3, 6, 7, 8, 9], de median is 6, de fourf wargest, and awso de fourf smawwest, number in de sampwe. For a continuous probabiwity distribution, de median is de vawue such dat a number is eqwawwy wikewy to faww above or bewow it.
The median is a commonwy used measure of de properties of a data set in statistics and probabiwity deory. The basic advantage of de median in describing data compared to de mean (often simpwy described as de "average") is dat it is not skewed so much by a smaww proportion of extremewy warge or smaww vawues, and so it may give a better idea of a "typicaw" vawue. For exampwe, in understanding statistics wike househowd income or assets, which vary greatwy, de mean may be skewed by a smaww number of extremewy high or wow vawues. Median income, for exampwe, may be a better way to suggest what a "typicaw" income is.
Because of dis, de median is of centraw importance in robust statistics, as it is de most resistant statistic, having a breakdown point of 50%: so wong as no more dan hawf de data are contaminated, de median wiww not give an arbitrariwy warge or smaww resuwt.
- 1 Finite data set of numbers
- 2 Probabiwity distributions
- 3 Popuwations
- 4 Jensen's ineqwawity for medians
- 5 Medians for sampwes
- 6 Muwtivariate median
- 7 Oder median-rewated concepts
- 8 Median-unbiased estimators
- 9 History
- 10 See awso
- 11 References
- 12 Externaw winks
Finite data set of numbers[edit]
The median of a finite wist of numbers can be found by arranging aww de numbers from smawwest to greatest.
If dere is an odd number of numbers, de middwe one is picked. For exampwe, consider de wist of numbers
- 1, 3, 3, 6, 7, 8, 9
This wist contains seven numbers. The median is de fourf of dem, which is 6.
If dere is an even number of observations, den dere is no singwe middwe vawue; de median is den usuawwy defined to be de mean of de two middwe vawues.[1][2] For exampwe, in de data set
- 1, 2, 3, 4, 5, 6, 8, 9
de median is de mean of de middwe two numbers: dis is , which is . (In more technicaw terms, dis interprets de median as de fuwwy trimmed mid-range).
The formuwa used to find de index of de middwe number of a data set of n numericawwy ordered numbers is . This eider gives de middwe number (for an odd number of vawues) or de hawfway point between de two middwe vawues. For exampwe, wif 14 vawues, de formuwa wiww give an index of 7.5, and de median wiww be taken by averaging de sevenf (de fwoor of dis index) and eighf (de ceiwing of dis index) vawues. So de median can be represented by de fowwowing formuwa:
where is an ordered wist of numbers, denotes its wengf, and and denotes de fwoor and ceiwing function, respectivewy.
|Aridmetic mean
|Sum of vawues of a data set divided by number of vawues:
|(1 + 2 + 2 + 3 + 4 + 7 + 9) / 7
|Middwe vawue separating de greater and wesser hawves of a data set
|1, 2, 2, 3, 4, 7, 9
|Most freqwent vawue in a data set
|1, 2, 2, 3, 4, 7, 9
One can find de median using de Stem-and-Leaf Pwot.
There is no widewy accepted standard notation for de median, but some audors represent de median of a variabwe x eider as x͂ or as μ1/2[1] sometimes awso M.[3][4] In any of dese cases, de use of dese or oder symbows for de median needs to be expwicitwy defined when dey are introduced.
The median is used primariwy for skewed distributions, which it summarizes differentwy from de aridmetic mean. Consider de muwtiset { 1, 2, 2, 2, 3, 14 }. The median is 2 in dis case, (as is de mode), and it might be seen as a better indication of centraw tendency (wess susceptibwe to de exceptionawwy warge vawue in data) dan de aridmetic mean of 4.
The median is a popuwar summary statistic used in descriptive statistics, since it is simpwe to understand and easy to cawcuwate, whiwe awso giving a measure dat is more robust in de presence of outwier vawues dan is de mean. The widewy cited empiricaw rewationship between de rewative wocations of de mean and de median for skewed distributions is, however, not generawwy true.[5] There are, however, various rewationships for de absowute difference between dem; see bewow.
Wif an even number of observations (as shown above) no vawue need be exactwy at de vawue of de median, uh-hah-hah-hah. Nonedewess, de vawue of de median is uniqwewy determined wif de usuaw definition, uh-hah-hah-hah. A rewated concept, in which de outcome is forced to correspond to a member of de sampwe, is de medoid.
In a popuwation, at most hawf have vawues strictwy wess dan de median and at most hawf have vawues strictwy greater dan it. If each set contains wess dan hawf de popuwation, den some of de popuwation is exactwy eqwaw to de median, uh-hah-hah-hah. For exampwe, if a < b < c, den de median of de wist {a, b, c} is b, and, if a < b < c < d, den de median of de wist {a, b, c, d} is de mean of b and c; i.e., it is (b + c)/2. As a median is based on de middwe data in a set, it is not necessary to know de vawue of extreme resuwts in order to cawcuwate it. For exampwe, in a psychowogy test investigating de time needed to sowve a probwem, if a smaww number of peopwe faiwed to sowve de probwem at aww in de given time a median can stiww be cawcuwated.[6]
The median can be used as a measure of wocation when a distribution is skewed, when end-vawues are not known, or when one reqwires reduced importance to be attached to outwiers, e.g., because dey may be measurement errors.
A median is onwy defined on ordered one-dimensionaw data, and is independent of any distance metric. A geometric median, on de oder hand, is defined in any number of dimensions.
The median is one of a number of ways of summarising de typicaw vawues associated wif members of a statisticaw popuwation; dus, it is a possibwe wocation parameter. The median is de 2nd qwartiwe, 5f deciwe, and 50f percentiwe. Since de median is de same as de second qwartiwe, its cawcuwation is iwwustrated in de articwe on qwartiwes. A median can be worked out for ranked but not numericaw cwasses (e.g. working out a median grade when students are graded from A to F), awdough de resuwt might be hawfway between grades if dere is an even number of cases.
When de median is used as a wocation parameter in descriptive statistics, dere are severaw choices for a measure of variabiwity: de range, de interqwartiwe range, de mean absowute deviation, and de median absowute deviation.
For practicaw purposes, different measures of wocation and dispersion are often compared on de basis of how weww de corresponding popuwation vawues can be estimated from a sampwe of data. The median, estimated using de sampwe median, has good properties in dis regard. Whiwe it is not usuawwy optimaw if a given popuwation distribution is assumed, its properties are awways reasonabwy good. For exampwe, a comparison of de efficiency of candidate estimators shows dat de sampwe mean is more statisticawwy efficient dan de sampwe median when data are uncontaminated by data from heavy-taiwed distributions or from mixtures of distributions, but wess efficient oderwise, and dat de efficiency of de sampwe median is higher dan dat for a wide range of distributions. More specificawwy, de median has a 64% efficiency compared to de minimum-variance mean (for warge normaw sampwes), which is to say de variance of de median wiww be ~50% greater dan de variance of de mean—see asymptotic efficiency and references derein, uh-hah-hah-hah.
Aho et. aw. give a divide-and-conqwer awgoridm to compute de f smawwest ewement of an unordered wist in winear time, which is faster dan sorting. Running it wif computes de median of .[7]
Probabiwity distributions[edit]
For any probabiwity distribution on de reaw wine R wif cumuwative distribution function F, regardwess of wheder it is any kind of continuous probabiwity distribution, in particuwar an absowutewy continuous distribution (which has a probabiwity density function), or a discrete probabiwity distribution, a median is by definition any reaw number m dat satisfies de ineqwawities
or, eqwivawentwy, de ineqwawities
in which a Lebesgue–Stiewtjes integraw is used. For an absowutewy continuous probabiwity distribution wif probabiwity density function ƒ, de median satisfies
Any probabiwity distribution on R has at weast one median, but in specific cases dere may be more dan one median, uh-hah-hah-hah. Specificawwy, if a probabiwity density is zero on an intervaw [a, b], and de cumuwative distribution function at a is 1/2, any vawue between a and b wiww awso be a median, uh-hah-hah-hah.
Medians of particuwar distributions[edit]
The medians of certain types of distributions can be easiwy cawcuwated from deir parameters; furdermore, dey exist even for some distributions wacking a weww-defined mean, such as de Cauchy distribution:
- The median of a symmetric unimodaw distribution coincides wif de mode.
- The median of a symmetric distribution which possesses a mean μ awso takes de vawue μ.
- The median of a normaw distribution wif mean μ and variance σ2 is μ. In fact, for a normaw distribution, mean = median = mode.
- The median of a uniform distribution in de intervaw [a, b] is (a + b) / 2, which is awso de mean, uh-hah-hah-hah.
- The median of a Cauchy distribution wif wocation parameter x0 and scawe parameter y is x0, de wocation parameter.
- The median of a power waw distribution x−a, wif exponent a > 1 is 21/(a − 1)xmin, where xmin is de minimum vawue for which de power waw howds[9]
- The median of an exponentiaw distribution wif rate parameter λ is de naturaw wogaridm of 2 divided by de rate parameter: λ−1wn 2.
- The median of a Weibuww distribution wif shape parameter k and scawe parameter λ is λ(wn 2)1/k.
Optimawity property[edit]
The mean absowute error of a reaw variabwe c wif respect to de random variabwe X is
Provided dat de probabiwity distribution of X is such dat de above expectation exists, den m is a median of X if and onwy if m is a minimizer of de mean absowute error wif respect to X.[10] In particuwar, m is a sampwe median if and onwy if m minimizes de aridmetic mean of de absowute deviations[11].
More generawwy, a median is defined as a minimum of
as discussed bewow in de section on muwtivariate medians (specificawwy, de spatiaw median).
This optimization-based definition of de median is usefuw in statisticaw data-anawysis, for exampwe, in k-medians cwustering.
Unimodaw distributions[edit]
It can be shown for a unimodaw distribution dat de median and de mean wie widin (3/5)1/2 ≈ 0.7746 standard deviations of each oder.[12] In symbows,
where |·| is de absowute vawue.
A simiwar rewation howds between de median and de mode: dey wie widin 31/2 ≈ 1.732 standard deviations of each oder:
Ineqwawity rewating means and medians[edit]
If de distribution has finite variance, den de distance between de median and de mean is bounded by one standard deviation.
This bound was proved by Mawwows,[13] who used Jensen's ineqwawity twice, as fowwows. We have
The first and dird ineqwawities come from Jensen's ineqwawity appwied to de absowute-vawue function and de sqware function, which are each convex. The second ineqwawity comes from de fact dat a median minimizes de absowute deviation function
This proof awso fowwows directwy from Cantewwi's ineqwawity.[14] The resuwt can be generawized to obtain a muwtivariate version of de ineqwawity,[15] as fowwows:
where m is a spatiaw median, dat is, a minimizer of de function The spatiaw median is uniqwe when de data-set's dimension is two or more.[16][17] An awternative proof uses de one-sided Chebyshev ineqwawity; it appears in an ineqwawity on wocation and scawe parameters.
Jensen's ineqwawity for medians[edit]
Jensen's ineqwawity states dat for any random variabwe x wif a finite expectation E(x) and for any convex function f
It has been shown[18] dat if x is a reaw variabwe wif a uniqwe median m and f is a C function den
A C function is a reaw vawued function, defined on de set of reaw numbers R, wif de property dat for any reaw t
is a cwosed intervaw, a singweton or an empty set.
Medians for sampwes[edit]
The sampwe median[edit]
Efficient computation of de sampwe median[edit]
Even dough comparison-sorting n items reqwires Ω(n wog n) operations, sewection awgoridms can compute de k'f-smawwest of n items wif onwy Θ(n) operations. This incwudes de median, which is de n/2'f order statistic (or for an even number of sampwes, de aridmetic mean of de two middwe order statistics).
Sewection awgoridms stiww have de downside of reqwiring Ω(n) memory, dat is, dey need to have de fuww sampwe (or a winear-sized portion of it) in memory. Because dis, as weww as de winear time reqwirement, can be prohibitive, severaw estimation procedures for de median have been devewoped. A simpwe one is de median of dree ruwe, which estimates de median as de median of a dree-ewement subsampwe; dis is commonwy used as a subroutine in de qwicksort sorting awgoridm, which uses an estimate of its input's median, uh-hah-hah-hah. A more robust estimator is Tukey's ninder, which is de median of dree ruwe appwied wif wimited recursion:[19] if A is de sampwe waid out as an array, and
- med3(A) = median(A[1], A[n/2], A[n]),
- ninder(A) = med3(med3(A[1 ... 1/3n]), med3(A[1/3n ... 2/3n]), med3(A[2/3n ... n]))
The remedian is an estimator for de median dat reqwires winear time but sub-winear memory, operating in a singwe pass over de sampwe.[20]
Easy expwanation of de sampwe median[edit]
In individuaw series (if number of observation is very wow) first one must arrange aww de observations in order. Then count(n) is de totaw number of observation in given data.
If n is odd den Median (M) = vawue of ((n + 1)/2)f item term.
If n is even den Median (M) = vawue of [(n/2)f item term + (n/2 + 1)f item term]/2
- For an odd number of vawues
As an exampwe, we wiww cawcuwate de sampwe median for de fowwowing set of observations: 1, 5, 2, 8, 7.
Start by sorting de vawues: 1, 2, 5, 7, 8.
In dis case, de median is 5 since it is de middwe observation in de ordered wist.
The median is de ((n + 1)/2)f item, where n is de number of vawues. For exampwe, for de wist {1, 2, 5, 7, 8}, we have n = 5, so de median is de ((5 + 1)/2)f item.
- median = (6/2)f item
- median = 3rd item
- median = 5
- For an even number of vawues
As an exampwe, we wiww cawcuwate de sampwe median for de fowwowing set of observations: 1, 6, 2, 8, 7, 2.
Start by sorting de vawues: 1, 2, 2, 6, 7, 8.
In dis case, de aridmetic mean of de two middwemost terms is (2 + 6)/2 = 4. Therefore, de median is 4 since it is de aridmetic mean of de middwe observations in de ordered wist.
Sampwing distribution[edit]
The distributions of bof de sampwe mean and de sampwe median were determined by Lapwace.[21] The distribution of de sampwe median from a popuwation wif a density function is asymptoticawwy normaw wif mean and variance[22]
where is de median of and is de sampwe size. For normaw sampwes, de density is , dus for warge sampwes de variance of de median eqwaws [23]
These resuwts have awso been extended.[24] It is now known for de -f qwantiwe dat de distribution of de sampwe -f qwantiwe is asymptoticawwy normaw around de -f qwantiwe wif variance eqwaw to
where is de vawue of de distribution density at de -f qwantiwe.
- Numericaw experimentation
In de case of a discrete variabwe, de sampwing distribution of de median for smaww-sampwes can be investigated as fowwows. We take de sampwe size to be an odd number . If a given vawue is to be de median of de sampwe den two conditions must be satisfied. The first is dat at most observations can have a vawue of or wess. The second is dat at most observations can have a vawue of or more. Let be de number of observations dat have a vawue of or wess and wet be de number of observations dat have a vawue of or more. Then and bof have a minimum vawue of 0 and a maximum of . If an observation has a vawue bewow , it is not rewevant how far bewow it is and conversewy, if an observation has a vawue above , it is not rewevant how far above it is. We can derefore represent de observations as fowwowing a trinomiaw distribution wif probabiwities , and . The probabiwity dat de median wiww have a vawue is den given by
Summing dis over aww vawues of defines a proper distribution and gives a unit sum. In practice, de function wiww often not be known but it can be estimated from an observed freqwency distribution, uh-hah-hah-hah. An exampwe is given in de fowwowing tabwe where de actuaw distribution is not known but a sampwe of 3,800 observations awwows a sufficientwy accurate assessment of .
Using dese data it is possibwe to investigate de effect of sampwe size on de standard errors of de mean and median, uh-hah-hah-hah. The observed mean is 3.16, de observed raw median is 3 and de observed interpowated median is 3.174. The fowwowing tabwe gives some comparison statistics. The standard error of de median is given bof from de above expression for and from de asymptotic approximation given earwier.
Sampwe size
|Expected vawue of median
|Standard error of median (above formuwa)
|Standard error of median (asymptotic approximation)
|Standard error of mean
The expected vawue of de median fawws swightwy as sampwe size increases whiwe, as wouwd be expected, de standard errors of bof de median and de mean are proportionate to de inverse sqware root of de sampwe size. The asymptotic approximation errs on de side of caution by overestimating de standard error.
In de case of a continuous variabwe, de fowwowing argument can be used. If a given vawue is to be de median, den one observation must take de vawue . The ewementaw probabiwity of dis is . Then, of de remaining observations, exactwy of dem must be above and de remaining bewow. The probabiwity of dis is de f term of a binomiaw distribution wif parameters and . Finawwy we muwtipwy by since any of de observations in de sampwe can be de median observation, uh-hah-hah-hah. Hence de ewementaw probabiwity of de median at de point is given by
Now we introduce de beta function, uh-hah-hah-hah. For integer arguments and , dis can be expressed as . Awso, . Using dese rewationships and setting bof and eqwaw to awwows de wast expression to be written as
Hence de density function of de median is a symmetric beta distribution over de unit intervaw which supports . Its mean, as we wouwd expect, is 0.5 and its variance is . The corresponding variance of de sampwe median is
However dis finding can onwy be used if de density function is known or can be assumed. As dis wiww not awways be de case, de median variance has to be estimated sometimes from de sampwe data.
- Estimation of variance from sampwe data
The vawue of —de asymptotic vawue of where is de popuwation median—has been studied by severaw audors. The standard "dewete one" jackknife medod produces inconsistent resuwts.[25] An awternative—de "dewete k" medod—where grows wif de sampwe size has been shown to be asymptoticawwy consistent.[26] This medod may be computationawwy expensive for warge data sets. A bootstrap estimate is known to be consistent,[27] but converges very swowwy (order of ).[28] Oder medods have been proposed but deir behavior may differ between warge and smaww sampwes.[29]
- Efficiency
The efficiency of de sampwe median, measured as de ratio of de variance of de mean to de variance of de median, depends on de sampwe size and on de underwying popuwation distribution, uh-hah-hah-hah. For a sampwe of size from de normaw distribution, de efficiency for warge N is
The efficiency tends to as tends to infinity.
In oder words, de rewative variance of de median wiww be , or 57% greater dan de variance of de mean – de standard error of de median wiww be 25% greater dan dat of de mean, uh-hah-hah-hah.[30]
Oder estimators[edit]
For univariate distributions dat are symmetric about one median, de Hodges–Lehmann estimator is a robust and highwy efficient estimator of de popuwation median, uh-hah-hah-hah.[31]
If data are represented by a statisticaw modew specifying a particuwar famiwy of probabiwity distributions, den estimates of de median can be obtained by fitting dat famiwy of probabiwity distributions to de data and cawcuwating de deoreticaw median of de fitted distribution, uh-hah-hah-hah.[citation needed] Pareto interpowation is an appwication of dis when de popuwation is assumed to have a Pareto distribution.
Coefficient of dispersion[edit]
The coefficient of dispersion (CD) is defined as de ratio of de average absowute deviation from de median to de median of de data.[32] It is a statisticaw measure used by de states of Iowa, New York and Souf Dakota in estimating dues taxes.[33][34][35] In symbows
where n is de sampwe size, m is de sampwe median and x is a variate. The sum is taken over de whowe sampwe.
Confidence intervaws for a two-sampwe test in which de sampwe sizes are warge have been derived by Bonett and Seier.[32] This test assumes dat bof sampwes have de same median but differ in de dispersion around it. The confidence intervaw (CI) is bounded inferiorwy by
where tj is de mean absowute deviation of de jf sampwe, var() is de variance and zα is de vawue from de normaw distribution for de chosen vawue of α: for α = 0.05, zα = 1.96. The fowwowing formuwae are used in de derivation of dese confidence intervaws
where r is de Pearson correwation coefficient between de sqwared deviation scores
- and
a and b here are constants eqwaw to 1 and 2, x is a variate and s is de standard deviation of de sampwe.
Muwtivariate median[edit]
Previouswy, dis articwe discussed de univariate median, when de sampwe or popuwation had one-dimension, uh-hah-hah-hah. When de dimension is two or higher, dere are muwtipwe concepts dat extend de definition of de univariate median; each such muwtivariate median agrees wif de univariate median when de dimension is exactwy one.[31][36][37][38]
Marginaw median[edit]
The marginaw median is defined for vectors defined wif respect to a fixed set of coordinates. A marginaw median is defined to be de vector whose components are univariate medians. The marginaw median is easy to compute, and its properties were studied by Puri and Sen, uh-hah-hah-hah.[31][39]
An awternative generawization of de median in higher dimensions is de centerpoint.
Interpowated median[edit]
When deawing wif a discrete variabwe, it is sometimes usefuw to regard de observed vawues as being midpoints of underwying continuous intervaws. An exampwe of dis is a Likert scawe, on which opinions or preferences are expressed on a scawe wif a set number of possibwe responses. If de scawe consists of de positive integers, an observation of 3 might be regarded as representing de intervaw from 2.50 to 3.50. It is possibwe to estimate de median of de underwying variabwe. If, say, 22% of de observations are of vawue 2 or bewow and 55.0% are of 3 or bewow (so 33% have de vawue 3), den de median is 3 since de median is de smawwest vawue of for which is greater dan a hawf. But de interpowated median is somewhere between 2.50 and 3.50. First we add hawf of de intervaw widf to de median to get de upper bound of de median intervaw. Then we subtract dat proportion of de intervaw widf which eqwaws de proportion of de 33% which wies above de 50% mark. In oder words, we spwit up de intervaw widf pro rata to de numbers of observations. In dis case, de 33% is spwit into 28% bewow de median and 5% above it so we subtract 5/33 of de intervaw widf from de upper bound of 3.50 to give an interpowated median of 3.35. More formawwy, if de vawues are known, de interpowated median can be cawcuwated from
Awternativewy, if in an observed sampwe dere are scores above de median category, scores in it and scores bewow it den de interpowated median is given by
For univariate distributions dat are symmetric about one median, de Hodges–Lehmann estimator is a robust and highwy efficient estimator of de popuwation median; for non-symmetric distributions, de Hodges–Lehmann estimator is a robust and highwy efficient estimator of de popuwation pseudo-median, which is de median of a symmetrized distribution and which is cwose to de popuwation median, uh-hah-hah-hah.[40] The Hodges–Lehmann estimator has been generawized to muwtivariate distributions.[41]
Variants of regression[edit]
The Theiw–Sen estimator is a medod for robust winear regression based on finding medians of swopes.[42]
Median fiwter[edit]
In de context of image processing of monochrome raster images dere is a type of noise, known as de sawt and pepper noise, when each pixew independentwy becomes bwack (wif some smaww probabiwity) or white (wif some smaww probabiwity), and is unchanged oderwise (wif de probabiwity cwose to 1). An image constructed of median vawues of neighborhoods (wike 3×3 sqware) can effectivewy reduce noise in dis case.[citation needed]
Cwuster anawysis[edit]
In cwuster anawysis, de k-medians cwustering awgoridm provides a way of defining cwusters, in which de criterion of maximising de distance between cwuster-means dat is used in k-means cwustering, is repwaced by maximising de distance between cwuster-medians.
Median–median wine[edit]
This is a medod of robust regression, uh-hah-hah-hah. The idea dates back to Wawd in 1940 who suggested dividing a set of bivariate data into two hawves depending on de vawue of de independent parameter : a weft hawf wif vawues wess dan de median and a right hawf wif vawues greater dan de median, uh-hah-hah-hah.[43] He suggested taking de means of de dependent and independent variabwes of de weft and de right hawves and estimating de swope of de wine joining dese two points. The wine couwd den be adjusted to fit de majority of de points in de data set.
Nair and Shrivastava in 1942 suggested a simiwar idea but instead advocated dividing de sampwe into dree eqwaw parts before cawcuwating de means of de subsampwes.[44] Brown and Mood in 1951 proposed de idea of using de medians of two subsampwes rader de means.[45] Tukey combined dese ideas and recommended dividing de sampwe into dree eqwaw size subsampwes and estimating de wine based on de medians of de subsampwes.[46]
Median-unbiased estimators[edit]
Any mean-unbiased estimator minimizes de risk (expected woss) wif respect to de sqwared-error woss function, as observed by Gauss. A median-unbiased estimator minimizes de risk wif respect to de absowute-deviation woss function, as observed by Lapwace. Oder woss functions are used in statisticaw deory, particuwarwy in robust statistics.
The deory of median-unbiased estimators was revived by George W. Brown in 1947:[47]
An estimate of a one-dimensionaw parameter θ wiww be said to be median-unbiased if, for fixed θ, de median of de distribution of de estimate is at de vawue θ; i.e., de estimate underestimates just as often as it overestimates. This reqwirement seems for most purposes to accompwish as much as de mean-unbiased reqwirement and has de additionaw property dat it is invariant under one-to-one transformation, uh-hah-hah-hah.— page 584
Furder properties of median-unbiased estimators have been reported.[48][49][50][51] Median-unbiased estimators are invariant under one-to-one transformations.
There are medods of constructing median-unbiased estimators dat are optimaw (in a sense anawogous to de minimum-variance property for mean-unbiased estimators). Such constructions exist for probabiwity distributions having monotone wikewihood-functions.[52][53] One such procedure is an anawogue of de Rao–Bwackweww procedure for mean-unbiased estimators: The procedure howds for a smawwer cwass of probabiwity distributions dan does de Rao—Bwackweww procedure but for a warger cwass of woss functions.[54]
The idea of de median appeared in de 13f century in de Tawmud [55][56] (furder[citation needed] for possibwe owder mentions)
The idea of de median awso appeared water in Edward Wright's book on navigation (Certaine Errors in Navigation) in 1599 in a section concerning de determination of wocation wif a compass. Wright fewt dat dis vawue was de most wikewy to be de correct vawue in a series of observations.
In 1757, Roger Joseph Boscovich devewoped a regression medod based on de L1 norm and derefore impwicitwy on de median, uh-hah-hah-hah.[57]
In 1774, Lapwace suggested de median be used as de standard estimator of de vawue of a posterior pdf. The specific criterion was to minimize de expected magnitude of de error; where is de estimate and is de true vawue. Lapwaces's criterion was generawwy rejected for 150 years in favor of de weast sqwares medod of Gauss and Legendre which minimizes to obtain de mean, uh-hah-hah-hah.[58] The distribution of bof de sampwe mean and de sampwe median were determined by Lapwace in de earwy 1800s.[21][59]
Antoine Augustin Cournot in 1843 was de first[60] to use de term median (vaweur médiane) for de vawue dat divides a probabiwity distribution into two eqwaw hawves. Gustav Theodor Fechner used de median (Centrawwerf) in sociowogicaw and psychowogicaw phenomena.[61] It had earwier been used onwy in astronomy and rewated fiewds. Gustav Fechner popuwarized de median into de formaw anawysis of data, awdough it had been used previouswy by Lapwace.[61]
Francis Gawton used de Engwish term median in 1881,[62] having earwier used de terms middwe-most vawue in 1869, and de medium in 1880.[63][64]
See awso[edit]
- Medoids which are a generawisation of de median in higher dimensions
- Centraw tendency
- Absowute deviation
- Bias of an estimator
- Concentration of measure for Lipschitz functions
- Median (geometry)
- Median graph
- Median search
- Median swope
- Median voter deory
- Weighted median
- ^ a b Weisstein, Eric W. "Statisticaw Median". MadWorwd.
- ^ Simon, Laura J.; "Descriptive statistics" Archived 2010-07-30 at de Wayback Machine, Statisticaw Education Resource Kit, Pennsywvania State Department of Statistics
- ^ David J. Sheskin (27 August 2003). Handbook of Parametric and Nonparametric Statisticaw Procedures: Third Edition. CRC Press. pp. 7–. ISBN 978-1-4200-3626-8. Retrieved 25 February 2013.
- ^ Derek Bisseww (1994). Statisticaw Medods for Spc and Tqm. CRC Press. pp. 26–. ISBN 978-0-412-39440-9. Retrieved 25 February 2013.
- ^ "Journaw of Statistics Education, v13n2: Pauw T. von Hippew". amstat.org.
- ^ Robson, Cowin (1994). Experiment, Design and Statistics in Psychowogy. Penguin, uh-hah-hah-hah. pp. 42–45. ISBN 0-14-017648-9.
- ^ Awfred V. Aho and John E. Hopcroft and Jeffrey D. Uwwman (1974). The Design and Anawysis of Computer Awgoridms. Reading/MA: Addison-Weswey. ISBN 0-201-00029-6. Here: Section 3.6 "Order Statistics", p.97-99, in particuwar Awgoridm 3.6 and Theorem 3.9.
- ^ "AP Statistics Review - Density Curves and de Normaw Distributions". Retrieved 16 March 2015.
- ^ Newman, Mark EJ. "Power waws, Pareto distributions and Zipf's waw." Contemporary physics 46.5 (2005): 323–351.
- ^ Stroock, Daniew (2011). Probabiwity Theory. Cambridge University Press. p. 43. ISBN 978-0-521-13250-3.
- ^ André Nicowas (https://maf.stackexchange.com/users/6312/andr%c3%a9-nicowas), The Median Minimizes de Sum of Absowute Deviations (The $ {L}_{1} $ Norm), URL (version: 2012-02-25): https://maf.stackexchange.com/q/113336
- ^ Basu, S.; Dasgupta, A. (1997). "The Mean, Median, and Mode of Unimodaw Distributions:A Characterization". Theory of Probabiwity and Its Appwications. 41 (2): 210–223. doi:10.1137/S0040585X97975447.
- ^ Mawwows, Cowin (August 1991). "Anoder comment on O'Cinneide". The American Statistician. 45 (3): 257. doi:10.1080/00031305.1991.10475815.
- ^ K.Van Steen Notes on probabiwity and statistics
- ^ Piché, Robert (2012). Random Vectors and Random Seqwences. Lambert Academic Pubwishing. ISBN 978-3659211966.
- ^ Kemperman, Johannes H. B. (1987). Dodge, Yadowah (ed.). "The median of a finite measure on a Banach space: Statisticaw data anawysis based on de L1-norm and rewated medods". Papers from de First Internationaw Conference Hewd at Neuchâtew, August 31–September 4, 1987. Amsterdam: Norf-Howwand Pubwishing Co.: 217–230. MR 0949228.
- ^ Miwasevic, Phiwip; Ducharme, Giwwes R. (1987). "Uniqweness of de spatiaw median". Annaws of Statistics. 15 (3): 1332–1333. doi:10.1214/aos/1176350511. MR 0902264.
- ^ Merkwe, M. (2005). "Jensen's ineqwawity for medians". Statistics & Probabiwity Letters. 71 (3): 277–281. doi:10.1016/j.spw.2004.11.010.
- ^ Bentwey, Jon L.; McIwroy, M. Dougwas (1993). "Engineering a sort function". Software—Practice and Experience. 23 (11): 1249–1265. doi:10.1002/spe.4380231105.
- ^ Rousseeuw, Peter J.; Bassett, Giwbert W. Jr. (1990). "The remedian: a robust averaging medod for warge data sets" (PDF). J. Amer. Statist. Assoc. 85 (409): 97–104. doi:10.1080/01621459.1990.10475311.
- ^ a b Stigwer, Stephen (December 1973). "Studies in de History of Probabiwity and Statistics. XXXII: Lapwace, Fisher and de Discovery of de Concept of Sufficiency". Biometrika. 60 (3): 439–445. doi:10.1093/biomet/60.3.439. JSTOR 2334992. MR 0326872.
- ^ Rider, Pauw R. (1960). "Variance of de median of smaww sampwes from severaw speciaw popuwations". J. Amer. Statist. Assoc. 55 (289): 148–150. doi:10.1080/01621459.1960.10482056.
- ^ Wiwwiams, D. (2001). Weighing de Odds. Cambridge University Press. p. 165. ISBN 052100618X.
- ^ Stuart, Awan; Ord, Keif (1994). Kendaww's Advanced Theory of Statistics. London: Arnowd. ISBN 0340614307.
- ^ Efron, B. (1982). The Jackknife, de Bootstrap and oder Resampwing Pwans. Phiwadewphia: SIAM. ISBN 0898711797.
- ^ Shao, J.; Wu, C. F. (1989). "A Generaw Theory for Jackknife Variance Estimation". Ann, uh-hah-hah-hah. Stat. 17 (3): 1176–1197. doi:10.1214/aos/1176347263. JSTOR 2241717.
- ^ Efron, B. (1979). "Bootstrap Medods: Anoder Look at de Jackknife". Ann, uh-hah-hah-hah. Stat. 7 (1): 1–26. doi:10.1214/aos/1176344552. JSTOR 2958830.
- ^ Haww, P.; Martin, M. A. (1988). "Exact Convergence Rate of Bootstrap Quantiwe Variance Estimator". Probab Theory Rewated Fiewds. 80 (2): 261–268. doi:10.1007/BF00356105.
- ^ Jiménez-Gamero, M. D.; Munoz-García, J.; Pino-Mejías, R. (2004). "Reduced bootstrap for de median". Statistica Sinica. 14 (4): 1179–1198.
- ^ Maindonawd, John; John Braun, W. (2010-05-06). Data Anawysis and Graphics Using R: An Exampwe-Based Approach. ISBN 9781139486675.
- ^ a b c Hettmansperger, Thomas P.; McKean, Joseph W. (1998). Robust nonparametric statisticaw medods. Kendaww's Library of Statistics. 5. London: Edward Arnowd. ISBN 0-340-54937-8. MR 1604954.
- ^ a b Bonett, DG; Seier, E (2006). "Confidence intervaw for a coefficient of dispersion in non-normaw distributions". Biometricaw Journaw. 48 (1): 144–148. doi:10.1002/bimj.200410148. PMID 16544819.
- ^ "Statisticaw Cawcuwation Definitions for Mass Appraisaw" (PDF). Iowa.gov. Archived from de originaw (PDF) on 11 November 2010.
Median Ratio: The ratio wocated midway between de highest ratio and de wowest ratio when individuaw ratios for a cwass of reawty are ranked in ascending or descending order. The median ratio is most freqwentwy used to determine de wevew of assessment for a given cwass of reaw estate.
- ^ "Assessment eqwity in New York: Resuwts from de 2010 market vawue survey". Archived from de originaw on 6 November 2012.
- ^ "Summary of de Assessment Process" (PDF). state.sd.us. Souf Dakota Department of Revenue - Property/Speciaw Taxes Division, uh-hah-hah-hah. Archived from de originaw (PDF) on 10 May 2009.
- ^ Smaww, Christopher G. "A survey of muwtidimensionaw medians." Internationaw Statisticaw Review/Revue Internationawe de Statistiqwe (1990): 263–277. doi:10.2307/1403809 JSTOR 1403809
- ^ Niinimaa, A., and H. Oja. "Muwtivariate median, uh-hah-hah-hah." Encycwopedia of statisticaw sciences (1999).
- ^ Moswer, Karw. Muwtivariate Dispersion, Centraw Regions, and Depf: The Lift Zonoid Approach. Vow. 165. Springer Science & Business Media, 2012.
- ^ Puri, Madan L.; Sen, Pranab K.; Nonparametric Medods in Muwtivariate Anawysis, John Wiwey & Sons, New York, NY, 197w. (Reprinted by Krieger Pubwishing)
- ^ Pratt, Wiwwiam K.; Cooper, Ted J.; Kabir, Ihtisham (1985-07-11). "Pseudomedian Fiwter". Architectures and Awgoridms for Digitaw Image Processing II. 0534: 34. Bibcode:1985SPIE..534...34P. doi:10.1117/12.946562.
- ^ Oja, Hannu (2010). Muwtivariate nonparametric medods wif R: An approach based on spatiaw signs and ranks. Lecture Notes in Statistics. 199. New York, NY: Springer. pp. xiv+232. doi:10.1007/978-1-4419-0468-3. ISBN 978-1-4419-0467-6. MR 2598854.
- ^ Wiwcox, Rand R. (2001), "Theiw–Sen estimator", Fundamentaws of Modern Statisticaw Medods: Substantiawwy Improving Power and Accuracy, Springer-Verwag, pp. 207–210, ISBN 978-0-387-95157-7.
- ^ Wawd, A. (1940). "The Fitting of Straight Lines if Bof Variabwes are Subject to Error" (PDF). Annaws of Madematicaw Statistics. 11 (3): 282–300. doi:10.1214/aoms/1177731868. JSTOR 2235677.
- ^ Nair, K. R.; Shrivastava, M. P. (1942). "On a Simpwe Medod of Curve Fitting". Sankhyā: The Indian Journaw of Statistics. 6 (2): 121–132. JSTOR 25047749.
- ^ Brown, G. W.; Mood, A. M. (1951). "On Median Tests for Linear Hypodeses". Proc Second Berkewey Symposium on Madematicaw Statistics and Probabiwity. Berkewey, CA: University of Cawifornia Press. pp. 159–166. Zbw 0045.08606.
- ^ Tukey, J. W. (1977). Expworatory Data Anawysis. Reading, MA: Addison-Weswey. ISBN 0201076160.
- ^ Brown, George W. (1947). "On Smaww-Sampwe Estimation". Annaws of Madematicaw Statistics. 18 (4): 582–585. doi:10.1214/aoms/1177730349. JSTOR 2236236.
- ^ Lehmann, Erich L. (1951). "A Generaw Concept of Unbiasedness". Annaws of Madematicaw Statistics. 22 (4): 587–592. doi:10.1214/aoms/1177729549. JSTOR 2236928.
- ^ Birnbaum, Awwan (1961). "A Unified Theory of Estimation, I". Annaws of Madematicaw Statistics. 32 (1): 112–135. doi:10.1214/aoms/1177705145. JSTOR 2237612.
- ^ van der Vaart, H. Robert (1961). "Some Extensions of de Idea of Bias". Annaws of Madematicaw Statistics. 32 (2): 436–447. doi:10.1214/aoms/1177705051. JSTOR 2237754. MR 0125674.
- ^ Pfanzagw, Johann; wif de assistance of R. Hamböker (1994). Parametric Statisticaw Theory. Wawter de Gruyter. ISBN 3-11-013863-8. MR 1291393.
- ^ Pfanzagw, Johann, uh-hah-hah-hah. "On optimaw median unbiased estimators in de presence of nuisance parameters." The Annaws of Statistics (1979): 187–193.
- ^ Brown, L. D.; Cohen, Ardur; Strawderman, W. E. A Compwete Cwass Theorem for Strict Monotone Likewihood Ratio Wif Appwications. Ann, uh-hah-hah-hah. Statist. 4 (1976), no. 4, 712–722. doi:10.1214/aos/1176343543. http://projecteucwid.org/eucwid.aos/1176343543.
- ^ Page 713: Brown, L. D.; Cohen, Ardur; Strawderman, W. E. A Compwete Cwass Theorem for Strict Monotone Likewihood Ratio Wif Appwications. Ann, uh-hah-hah-hah. Statist. 4 (1976), no. 4, 712–722. doi:10.1214/aos/1176343543. http://projecteucwid.org/eucwid.aos/1176343543.
- ^ Tawmud and Modern Economics
- ^ Modern Economic Theory in de Tawmud by Yisraew Aumann
- ^ Stigwer, S. M. (1986). The History of Statistics: The Measurement of Uncertainty Before 1900. Harvard University Press. ISBN 0674403401.
- ^ Jaynes, E.T. (2007). Probabiwity deory : de wogic of science (5. print. ed.). Cambridge [u.a.]: Cambridge Univ. Press. p. 172. ISBN 978-0-521-59271-0.
- ^ Lapwace PS de (1818) Deuxième suppwément à wa Théorie Anawytiqwe des Probabiwités, Paris, Courcier
- ^ Howarf, Richard (2017). Dictionary of Madematicaw Geosciences: Wif Historicaw Notes. Springer. p. 374.
- ^ a b Keynes, J.M. (1921) A Treatise on Probabiwity. Pt II Ch XVII §5 (p 201) (2006 reprint, Cosimo Cwassics, ISBN 9781596055308 : muwtipwe oder reprints)
- ^ Gawton F (1881) "Report of de Andropometric Committee" pp 245–260. Report of de 51st Meeting of de British Association for de Advancement of Science
- ^ encycwopediaofmaf.org
- ^ personaw.psu.edu
Externaw winks[edit]
- Hazewinkew, Michiew, ed. (2001) [1994], "Median (in statistics)", Encycwopedia of Madematics, Springer Science+Business Media B.V. / Kwuwer Academic Pubwishers, ISBN 978-1-55608-010-4
- Median as a weighted aridmetic mean of aww Sampwe Observations
- On-wine cawcuwator
- Cawcuwating de median
- A probwem invowving de mean, de median, and de mode.
- Weisstein, Eric W. "Statisticaw Median". MadWorwd.
- Pydon script for Median computations and income ineqwawity metrics
- Fast Computation of de Median by Successive Binning
- 'Mean, median, mode and skewness', A tutoriaw devised for first-year psychowogy students at Oxford University, based on a worked exampwe.
- The Compwex SAT Maf Probwem Even de Cowwege Board Got Wrong: Andrew Daniews in Popuwar Mechanics
This articwe incorporates materiaw from Median of a distribution on PwanetMaf, which is wicensed under de Creative Commons Attribution/Share-Awike License.


text:
$2300 week
10 Bulleen Road, balwyn north VIC
- 5
- 5
- 2
$2300 a week
10 Bulleen Road, balwyn north VIC
- 5
- 5
- 2
Luxury living in Balwyn NorthThis luxury french provincial family home with its elegant high-end interiors, premium fittings and quality finishes make this a must have home. Just a short walk to the North Balwyn Village and in Balwyn High School Zone, access to buses and tram are at the door, shops and eateries just around the corner. Walk to Balwyn High, Balwyn North Primary and St Bede's Primary. Myrtle and Macleay Parks are nearby, as is the Koonung Creek Trail and entry to the Eastern Freeway.
Ground floor includes a formal living area, a private rumpus/theatre room and expansive kitchen/family/meals area. Kitchen come complete with a butler's pantry, integrated fridge and freezer. A master bedroom equipped with ensuite and walk in robe.
First floor features a spectacular grand staircase with two rumpus rooms provids further family living options. A gallery leads to the full master bedroom suite comprising a luxurious ensuite bathroom, retreat space, balcony and large fully fitted dressing room. Upstairs also features a further three bedrooms all with their very own ensuite and walk in robe.
The home offers:
- Five spacious bedrooms all with ensuites
- Six living areas including three rumpus,one separate living and open plan living & dining
- Master ensuite with double vanity, double shower and freestanding bath
- Kitchen with butler's pantry and integrated fridge and freezer
- Ducted heating and ducted air-conditioning
- Undercover alfresco terrace and solar heated lap pool
- Garden maintenance included
Please book an inspection time or contact the agent if you would like to inspect this property.
By registering for an inspection, you will be instantly informed of any updates, changes or cancellations to the inspection time.
The fastest and easiest way to apply for this property is through 1Form using the Apply Online feature, you will need an application code to apply, supplied after you have inspected the property.
Please wait while we submit your enquiry
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subset: commoncrawl


text:
On September 12th, VIXX's HongBin shares a funny and interesting moment he had regarding Apple airpods on their official fancafe chatting room.
HongBin first shared that he is interested in getting an iPhone but does not like the headphone jack. However, compared to using Apple airpods, he has another concern. He revealed that he had actually picked up the members' airpods which they had lost countless times.
Through such incidents, HongBin decided that he would not get them, suggesting that he might also be losing them in the future if he actually got them.
In addition to that, since it is not easy to identify whose airpods belong to who, he also shared how two different songs may be coming from the airpods once plugged into their ears.
Seeing the cute confession from HongBin, many fans were laughing and also liking how adorable he was. They also thought that the VIXX members must have had a hilarious moment especially when two different songs came out from a pair of airpods.
Nonetheless, they also wished that HongBin would make a wise decision when getting a new phone.
Do you find it funny too?
Read More : VIXX N's Kiss Scene In Drama "Familiar Wife"?
he is so sweet. in fancafe it always feel like we are talking to a friend


text:
UK-based foreign exchange and payments specialist Currency Matters joins IBM Blockchain World Wire — the global payments network which uses Stellar's XLM cryptocurrency.
In a press release on Friday, Currency Matters announced its intention to join World Wire, IBM and Stellar's real-time cross-border payments network.
Boasting a global reach, with clients in 76 countries payments in over 100 jurisdictions, foreign exchange specialists Currency Matters intends to upgrade their systems with the World Wire network — enabling them to settle cross-border payments in mere seconds, at a fraction of the cost. This will allow the company and its clients access to new digital assets, including Stellar's XLM cryptocurrency and the stable coins that are built on it.
Speaking in the press release, Currency Matters CEO Jon Anderson emphasized the importance of the new technology:
"Working with IBM, Currency Matters will help to deliver a faster, more transparent, and secure cross border payments process at a much lower cost. This technology will revolutionise the global payments industry and we are delighted to play our part."
IBM announced the launch of the World Wire network on Monday, and is already positioned to support more than 70 countries, with over 1000 trading pairs and 40+ banking end points. The cross-border payments network — built on IBM's blockchain technology and the Stellar public protocol — is poised to be at the forefront of the global remittances and settlements sector.


text:
Please reload this page to view signature.
NIKE rocks....................!
"Don't wait for the Perfect moment.. take the Moment and make it Perfect."
Mariasharapova Rocksssssss
Life is 10% what happens to you and 90% how you react to it.
i hate nike...........
Best Line Written in front of a masjid in New york
''Always believe in God,bcoz some questions in grave that cannot be answered by Google''


text:
Tammy Abraham and Olivier Giroud seem to be the two players competing to start for Frank Lampard this season, and both will likely get their chance this week.
Tammy played on Sunday against Manchester United, and Olivier will surely play at least one of the two upcoming games this week, having also come on in the United game.
Lampard appears to have opted for Abraham because of his superior ability to join in the press, and he did run enthusiastically.
But he didn't hold the ball up too well, or play his teammates in with as much quality as Olivier Giroud might have.
The conundrum will go on for Frank until one of the two settles in as number one. It would only take Tammy a couple of goals to convince the fans to give him a bit of time, but until he starts scoring the pressure to play the more experienced Giroud will only grow.


text:
The transcripts of the trial of Charles Taylor, former President of Liberia.
I've not done it normally before, so I'm asking to be present.
j previous speech
k next speech
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text:
TETA ANA – 6 people
Teta Ana is a cool looking apartment for, fully furnished, featuring free WiFi and Air-conditioning. Situated in the same building as Apartments Braco, it is on the second floor and can accommodate 6 people with the possibility to add extra bed for one more.
Shops, bars and restaurants and Novalja's centre are 600m far from the apartment Teta Ana. Famous party beach Zrce is only 2km away and it is best to come with a local bus or a private transport.
The Island of Pag has many beautiful gems that are easy to see if you have a private transport. It can be organized for you from any airport close to the Island Pag.
1 Bedroom – Double, sleeps 2 / Living room – 2 Sofa bed, sleeps 4 / 1 Bathroom / Kitchen / Balcony
Air conditioning / Wi-Fi / Parking / TV / Linen & Towels provided
Transport (taxi-van), additional fee
Beach: 70m
Restaurant: 100m
Bus stop: 70m
Supermarket Plodine: 750m
Novalja's centre: 650m
Zrce Beach: 2km


text:
Telephony Support Service (VoIP)
About the Service
The Telephony Support Service (VoIP) offers support for Voice over IP (VoIP) systems installed by BT Lancashire Services. Our VoIP systems are designed to provide internal phone extensions and to link to your external phone lines and your current telephone number.
VoIP telephony allows your school to make telephone calls between the internal phone extensions and externally, using your existing IT network data cabling to deliver the telephony internally around your school. This reduces the need for separate internal telephone cables and associated expense, making it easier to expand the school's internal telephone system. The service uses a server to act as a PBX (Private Branch Exchange or internal telephone exchange), which also reduces the costs associated with buying and operating a physical PBX.
What are the benefits?
VoIP technology enables the school to have any number of internal telephone extensions and potentially reduces the number of external lines, reducing costs and improving internal communication. The VoIP phones plug into network data points (the same type of socket PCs plug into).
Future expansion is more cost effective than with a dedicated telephone system using its own cabling. Using PoE+ (Power over Ethernet) switches also removes the need for power cables and adapters for the telephone handsets, freeing power sockets for use by other devices or the need to have additional electrical sockets installed.


text:
Comment on Reader Questions: How was your life as a Single? by Victoria.
Nice one Ufuomaee. Could you give us a glimpse of what happened with regards to simglehood in between that marriage and your present happier one.
Recent Comments by Victoria
Perfect Love 24
Hmm. Would she have made all this effort if she hadn't also cheated we well? What if it was only him in the wrong?
Did her feelings for her ex just disappear? And why should Temi be angry when he did the same thing himself?
The House Girl – The Epilogue
Beautifully scripted as always Ufuomaee. A wonderful story of grace and redemption
A Small World: Season Two – Three Weddings And A Funeral (Episode 29)
Nice one. Can Temi confront Oyinda already? Sin thrives in secrecy. He's gotten away with it too many times and someone needs to show him a mirror.
Categories: Uncategorised


text:
News Corp is a network of leading companies in the worlds of diversified media, news, education, and information services.
Simpson thinks Leicester can repeat stunning title triumph if they beat City away
Gundogan slots pen past Schmeichel as City come from behind
Furious Man City only found out Arteta had been named Arsenal manager on TV
Classy Kevin de Bruyne and wife surprise kids in hospital with Xmas presents
Arteta promises 'fast flowing, attacking football' as he's confirmed Arsenal boss
Guardiola 'demanding three new transfers' if he is to sign new Man City contract
Pochettino refusing to commit to Real - as he wants to see if Man City are keen
Man City ace Sterling says phenomenal goal record means nothing with no trophies
Arteta so obsessed with football he held baby while getting physio on knees
Mahrez vows to recapture Player of the Year form after inconsistent 18 months
Man Utd and City hold talks over £111m-rated Leverkusen ace Havertz
Arteta gives emotional farewell speech at Man City as he moves to Arsenal
'Removal van' spotted at Arteta's house as incoming Arsenal boss prepares for move
Arteta to be named Arsenal boss in next 48 hrs as City haggle over compensation
Who is Rodolfo Borrell and will he be Mikel Arteta's assistant at Arsenal?
Premier League selections including City vs Leicester and Watford vs United
PSG 'line-up move' for Man City boss Pep Guardiola to replace Thomas Tuchel
Arsenal slammed by Man City over shambolic and disrespectful pursuit of Arteta


text:
by Dan Kolber
Post No. 2,950 The following is brought to you by Intellivest Securities Research, Inc. Toward the end of this Blog is a list of the Dow 30 current CEOs, and a recent ranking of the Dow 30 components by market capitalization and a summary of recent Dow 30 components' SEC filings.
A read of the print editions of Thursday's Wall Street Journal, Financial Times, Investor's Business Daily, New York Times, USA Today, Atlanta Journal & Constitution & Daily Report (Ga. - carries Bloomberg) yielded the following stories about Dow Jones Industrial Average 30 component companies and the Dow with stories about the Dow aggregated first and then items about Dow Jones Industrial Average 30 companies presented alphabetically, followed by a separate table of Dow component's symbol and Wednesday's closing stock prices and related data in alphabetical order.
The Dow Jones Industrial Average: The Dow Jones Industrial Average closed Wednesday at 17533.15 down 268.05 or 1.51% from Tuesday's close of 17801.20. For the year the Dow is up 5.77%. Of the Dow components only Nike gained and 29 declined. The only and therefore biggest gainer dollar-wise and percentage-wise was Nike up 63 cents or 0.65%. The biggest decliner dollar-wise and percentage-wise was Boeing down $5.02 or 3.87%.
WSJ pC4 "Stocks slide broadly as crude oil price falls" by Dan Strumpf, Saumya Vaishampayan says all 10 major sectors declined but hardest hit were energy producers as Chevron fell $2.15 and Exxon lost 2.71.
FT p23 "Wall street" says US equity markets slid for a 3rd day as the energy sector remained under pressure.
NYT pB3 "Plunging oil prices take Wall st. lower" by AP says the 3 main market indexes fell at least 1.5% as Exxon and Chevron both dropped.
IBD pB3 "Uptrend feels pressure as indexes fall sharply" by David Saito-Chung says the plunge in oil to nearly $60 a barrel shook confidence among investors as Wednesday's action saw sharp losses, mixed trade while the current outlook is uptrend under pressure.
As of the open of the market on Thursday the current divisor for the Dow Jones Industrial Average found at page C6 of Thursday's Wall St. Journal is 0.15571590501117. Thursday's trailing P/E ratio is 16.91 down from yesterday's trailing P/E ratio of 16.96 (last year it was 16.27). Today's P/E estimate is 15.75 unchanged from Wednesday's P/E estimate of 15.75 (year ago it was 15.00) and today's dividend yield is 2.17 unchanged from Wednesday's dividend yield of 2.17 (last year it was 2.12). The Dow's all-time high was 17958.79 on December 5, 2014. The 12 year low close for the Dow was on March 9, 2009 when it fell to 6,547.05.
Wednesday's Dow Jones Industrial Average numerator is 2730.19 down 41.74 from Tuesday's numerator of 2771.93. This is the sum of all 30 closing prices. A short cut to the Dow numerator is to multiply the closing Dow by the Divisor. Now, if you divide the Dow numerator change for today by the divisor (0.15571590501117) you get the change in today's Dow. A dollar increase or decrease in a Dow stock results in a $6.42 change in the Dow Index.
The average closing price (the closing numerator divided by 30) of Wednesday's Dow Jones Industrial Average was $91.01 down $1.39 from Tuesday's average closing price of $92.40. The median closing price of Wednesday's Dow Jones Industrial Average was $90.82 (MCD/DIS) down $1.34 from Tuesday's median closing price of $92.16 (XOM/DIS). The lowest volume was Travelers and the highest volume was GE.
If Wednesday morning before the market opened you had purchased 100 shares of each of the Dow Jones Industrial Average 30 shares (assuming you could buy fractional shares and assuming no transaction costs or dividends) and sold at the close you would have lost $4,174 ($277,193- $273,019).
12/10/14 Wed. 4:36 pm MarketWatch by Anora Mahmudova & Barbara Kollmeyer says
U.S. stocks suffered their worst declines in about two months on Wednesday as a renewed slump in oil prices slammed energy companies while investors fretted that a stunning drop in oil prices signals a more worrisome global-economic slowdown.The S&P 500 SPX, -1.64% index fell 33.68 points, or 1.6%, to 2,026.14, its biggest one-day percentage drop since Oct 13. CLF5, +0.38% Companies whose profits depend heavily on the price of oil were hit the hardest, but materials and industrials sold off as slowing spending by energy companies began to spread to related entities like oil-field services and suppliers. The S&P 500 energy sector dropped 6% over the past three trading sessions. Meanwhile, ExxonMobil Corp XOM, -2.97% and Chevron Corp CVX, -2.01% were among the top decliners on the Dow Jones Industrial Average DJIA, -1.51% which dropped 268.05 points, or 1.5%, to 17,533.15. The Nasdaq Composite COMP, -1.73% ended the day with a loss of 82.44 points, or 1.7%, to 4,684.03. The Russell 2000 RUT, -2.20% dropped 26 points, or 2.2%, to 1,161.86, erasing all of Tuesday's gains. Small and mid-cap energy companies were among the biggest decliners.
The losses on Wall Street come after seven consecutive weeks of gains for the S&P 500 and Dow industrials. Implied volatility on the S&P 500 jumped 24% to above 18, the highest level since Oct 20.The top four decliners on the S&P 500 were energy companies, including ONEOK, Inc OKE, -7.79% and Cheasapeake Energy Corp CHK, -6.59% down 7.8% and 6.6% respectively.
Kristina Hooper, U.S. investment strategist at Allianz Global Investors, said that until oil prices stabilize, stock markets will continue to be volatile, though she pointed out that moves are still relatively small. "Investors have not made up their mind whether to attribute the fall in oil to oversupply or to demand issues and right now they are gripped with fear that the global economy is slowing and that the U.S. is not immune to that," Hooper said.The major story of the moment was oil, which slumped further Wednesday on data showing a surprise increase in U.S. supplies. Oil prices already had been down more than 2% earlier in the day after the Organization of Petroleum and Exporting Countries lowered its forecast for 2015, and also said non-OPEC supply will rise more than forecast next year. WTI crude oil prices for January delivery CLF5, +0.38% settled 4.5% down at $60.94, while January Brent LCOF5, -3.76% futures, on Wednesday, ended at a fresh five-year low.
Thursday's Dow News followed by Wednesday's Closing Dow Numbers:
AT&T: NYT pF1 "Buy. Divide. Conquer" by Andrew Ross Sorkin discusses the cycle of mergers and gives examples of AT&T break up and Procter & Gamble's divestiture of Duracell.
American Express: No mentions found.
Boeing: No mentions found.
Caterpillar: No mentions found.
Chevron: WSJ pC4 "Stocks slide broadly as crude oil price falls" by Dan Strumpf, Saumya Vaishampayan says all 10 major sectors declined but hardest hit were energy producers as Chevron fell $2.15 and Exxon lost 2.71. Chevron is charted under Bad News.
Daily Report p1 "Chevron GC: "I'm confident we're right" in epic case" by R. Robin McDonald says Chevron has spent more than $200 mil defending itself and fighting to overturn a $9.5 bil judgment in Ecuador.
NYT pB3 "Plunging oil prices take Wall st. lower" by AP says the 3 main market indexes fell at least 1.5% as Exxon and Chevron both dropped.
Cisco: IBD pA2 "Tech firms warn FCC on rules, WSJ pB6 "Tech gear firms warn FCC on Internet rules" by Drew Fitzgerald say Cisco, Intel and IBM says proposed rule changes to reclassify broadband access as a utility would have a negative impact on the industry.
IBD pA5 "Cisco Systems darts into data analytics" by Pete Barlas says Cisco is making software for firms to find and analyze data from multiple sources.
Coke: No mentions found.
Disney: WSJ pB7 "Novel Dish channel strategy" by Shalini Ramachandran, Joe Flint says Disney's ABC is the only major broadcaster that has a deal in place for Dish for its new online TV service.
DuPont: No mentions found.
Exxon: WSJ pC4 "Stocks slide broadlyas crude oil price falls" by Dan Strumpf, Saumya Vaishampayan says all 10 major sectors declined but hardest hit were energy producers as Chevron fell $2.15 and Exxon lost 2.71.
NYT pB3 "Plunging oil prices take Wall st. lower" by AP says the 3 main market indexes fell at least 1.5% as Exxon and Chevron both dropped.
GE: WSJ pB2 "How cheaper oil helps US factories" by Timothy Aeppel says GE in Oct. cut projections for future growth in its oil and gas business.
Goldman Sachs: No mentions found.
Home Depot: No mentions found.
Intel: IBD pA2 "Tech firms warn FCC on rules, WSJ pB6 "Tech gear firms warn FCC on Internet rules" by Drew Fitzgerald say Cisco, Intel and IBM says proposed rule changes to reclassify broadband access as a utility would have a negative impact on the industry.
IBD pA5 "Intel, Qualcomm accelerate their efforts in China" by Michael Perrault says Intel expected approval early next year to pay $1.5 bil for 20% of Tsinghua Unigroup, a Chinese group that owns chipmakers.
IBM: IBD pA2 "Tech firms warn FCC on rules, WSJ pB6 "Tech gear firms warn FCC on Internet rules" by Drew Fitzgerald say Cisco, Intel and IBM says proposed rule changes to reclassify broadband access as a utility would have a negative impact on the industry.
IBD pA2 "Apple, IBM Mobile First debuts" says the 1st MobileFirst for Apple iOS platform products was delivered.
JPMorgan: WSJ pC10 "Big banks' derivatives hose trade" by David Reilly, WSJ pA4 "A primer on derivatives provision anks seek" by Victoria McGrane say JPMorgan and other big banks are lobbying to gut rules under Dodd-Frank regulating derivatives.
Johnson & Johnson: No mentions found.
McDonald's: WSJ pB1 "McDonald's to whittle down menu" by Julie Jargo, AJC pA16 "McDonald's to trim menu, ingredients", IBD pA2 "McDonald's vows to slim menu" say McDonald's will remove 8 items and allow more customization in ordering.
Merck: WSJ pB4 "DA approves Merck's broader HPV vaccine" by Peter Loftus, AJC pA16 "Vaccine blocks five additional HPV strains", IBD pA2 "Mcerck repurposes cancer drug, say US regulators approved Gardasil 9 vaccine designed to offer broader protection than existing vaccines versus cervical cancer and other cancers caused by a sexually transmitted virus.
Microsoft: No mentions found.
Nike: No mentions found.
Pfizer: No mentions found.
Procter & Gamble: NYT pF1 "Buy. Divide. Conquer" by Andrew Ross Sorkin discusses the cycle of mergers and gives examples of AT&T break up and Procter & Gamble's divestiture of Duracell.
3M: No mentions found.
Travelers: No mentions found.
United Technologies: No mentions found.
UnitedHealthcare: No mentions found.
Verizon: No mentions found.
Visa: No mentions found.
Walmart: NYT pB10 "Walmart illegally punished workers, judge rules" by Steven Greenhouse says the NLRB says Walmart illegally disciplined employees for going on strike and illegally threatened to close a store of employees unionized.
Wednesday's Closing Dow Numbers:
|Last Sale
|% Change
|Share Volume
Here are the current CEOs of the Dow 30 Companies:
AT&T T Randall L. Stephenson (Dallas, TX)
American Express AXP Kenneth I. Chenault (NY, NY)
Boeing BA W. James McNerney, Jr. (Chicago, Ill)
Caterpillar CAT Douglas Oberhelman (Peoria, Ill.)
Chevron CVX John Watson (San Ramon, CA)
Cisco CSCO John Chambers (San Jose, CA)
Coca Cola KO Muhtar Kent (Atlanta, GA)
Disney DIS Robert Iger (Burbank, CA)
DuPont DD Ellen Kullman (Wilmington, DE)
ExxonMobil XOM Rex W. Tillerson (Irving, Tx)
GE Jeffrey R. Immelt (Fairfield, CT)
Goldman Sachs GS Lloyd Blankfein (NY, NY)
Home Depot HD Craig Menear (Atlanta, GA)
Intel INTC Brian Krzanich (Santa Clara, CA)
IBM Virginia M. Rometty (Armonk, NY)
JPMorgan Chase JPM Jamie Dimon (NY, NY)
Johnson & Johnson JNJ Alex Gorsky (New Brunswick, NJ)
McDonald's MCD Donald Thompson (Oak Brook, Ill)
Merck MRK Kenneth Frazier (Whitehouse Station, N.J.)
Microsoft MSFT Satya Nadella (Redmond, WA)
Nike NK Mark Parker (Beaverton, OR)
Pfizer PFE Ian Read (NY, NY)
Procter & Gamble PG A. G. Lafley (Cincinnati, OH)
3M MMM Inge Thulin (St. Paul, MN)
Travelers TRV Jay S. Fishman (NY, NY)
UnitedHealthUNC Stephen Hemsley (Minnetonka, MN)
United Technologies UTX Greg Hayes (Hartford, CT)
Verizon VZ Lowell McAdam (NY, NY)
Visa V Charles W. Scharf (Foster City, CA)
Wal-Mart WMT Doug McMillon (Bentonville, ARK)
Here are the Dow Jones Industrial Average 30 as of close of business 11/6/14 ranked in order of market capitalization in billions:
1. Exxon Mobil XOM $407.66
2. Microsoft MSFT 401.43
3. Johnson & Johnson JNJ 305.13
5. Wal-Mart WMT 250.74
6. Procter & Gamble PG 240.22
7. JPMorgan Chase JPM 229.94
8. Chevron CVX 225.08
9. Verizon VZ 208.65
10. Pfizer PFE 190.48
11. Coke KO 185.23
13. Merck MRK 170.94
14. Intel INTC 163.52
16. Disney DIS 157.92
17. Visa V 157.12
18. Home Depot HD 130.94
19. Cisco CSCO 128.81
21. United Technologies UTX 98.99
22. American Express AXP 95.33
23. UnitedHealth UNH 94.48
24. McDonald's MCD 92.95
25. Boeing BA 88.82
26. Goldman Sachs GS 86.48
27. Nike NKE 81.50
28. DuPont DD 63.53
29. Caterpillar CAT 61.71
30. Travelers TRV 33.77
Here are the latest 8K, 10Q & 10K & Proxy & certain other SEC filings as of close of business 11/6/14:
Symbol & Co. Name/Date of Filing/Form Filed/ Comments
10/24/14 8K re: completion of sale of Ct. wireline operations to Frontier Comm
3 8Ks (10/22; 10/22 & 9/30/14) re: 3Qtr result
8/1/14 10Q & 7/24/14 8K & 7/23/14 8K re: qtr ended 6/30
American Express AXP:
10/28/14 10Q & 10/15/14 8K re: 3Qtr results ended 9/30/14
10/15/14 8K re: delinq. & write-off stats for 3 months ended 9/30/14
9/30/14 8K re: appointment of Neal Sample as Pres., Enterprise Growth
9/15/14 8K re: delinq. & write-off stats for 3 months end 8/31/14
8/15/14 8K re: delinq. & write-off stats for 3 months end 7/31/14
Boeing BA:
10/31/14 8K re: issuance of senior notes
10/22/14 10Q & 10/22/14 8K re: 3Qtr results ended 9/30/14
10/16/14 8K re: credit agreements
Caterpillar CAT:
10/31/14 10Q & 10/23/14 8K re: 3Qtr results ended 9/30/14
10/22/14 8K re: sales to retail and OEM
10/14/14 8K re: retirement of Group Presidents Stuart Levenick & Steven Wunning
9/30/14 8K re: price changes
9/19/14 8K re: info re: retail sales of OEMs
9/16/14 8K re: credit agreement with Citibank up to $3.15 bil
8/20/14 8K re: rolling 3 month retail sales stats
8/1/14 10Q & 7/24/14 8K re: 2Q ended 6/30/14
Chevron CVX:
10/31/14 8K re: 3Qtr results
8/14/14 8K re: voluntary dismissal of shareholder derivative lawsuit
8/6/14 10Q & 8/1/14 8K & 7/10/14 8K re: 2Q ended 6/30/14
Cisco CSCO:
9/30/14 2 Proxy filings re: Annual Shareholde Meeting to be held 11/20/14 at 9am at Cisco Building, San Jose, CA
9/12/14 8K re: departure of director Marc Benioff & reduction of board to 10
9/9/14 10K & 8/13/14 8K re: results for year ended 7/26/14
8/14/14 8K re: restructuring plan & lay-offs of 6,000 or 8% of global workforce
Coke KO:
10/29/14 10Q & 10/21/14 8K re: 3Qtr ended 9/26/14
10/1/14 8K re: Guidelines for '14 Equity Plan
9/22/14 & 9/19/14 8Ks re: close of public offering of long term notes
8/20/14 8K re: purchase of 16.7% state in Monster
Disney DIS:
11/6/14 8K re: 4Qtr & FY ended 9/27/14
10/3/14 8K re: CEO Robert Iger's amended employment contract
8/5/14 10Q for quarter ended 6/28/14
8/5/14 & 8/5 8K re: 10Q for 3Qtr ended 6/28/14
DuPont DD:
10/28/14 CEO letter to shareholders
10/28/14 & 10/28/14 8K re: 3Qtr ended 9/30/14
8/5/14 8K re: election of Ulf M. Mark Scheider
ExxonMobil XOM:
11/5/14 10Q & 10/31/14 8K re: 3Qtr ended 9/30/14
8/6/14 10Q & 7/31/14 8K re: 2Qtr ended 6/30/14
8/6/14 8K re: retirement of P.T. Mulva as VP/controller to be replaced by D.S. Rosenthal
11/4/14 10Q & 10/17/14 8K re: 3Qtr ended 9/30/14
Goldman Sachs GS:
11/5/14 10Q & 10/16/14 8K re: 3Qtr ended 9/30/14
10/23/14 8K re: legal opinion re: debt issuance
8/25/14 8K re: settlement with FHFA re: sale of residential mortgage backed securities to Fannie Mae & Freddie Mac
8/7/14 10Q & 7/15/14 8K re: 2Qtr ended 6/30/14
Home Depot HD:
11/6/14 8K re: breach of payment data system
10/20/14 8-K/A re: promotion of Craig A. Menear to CEO
10/14/14 8K re: resignation of Marvin R. Ellison, EVP
9/18/14 8K re: update on guidance due to data breach
9/8/14 8K re: breach od payment data systems
8/27/14 10Q & 8/19/14 8K results for quarter ended 8//14
8/21/14 8K re: election of Craig A. Menear as CEO &Pes. and Frank Blake taking on as chairman eff. 11/1/14 & amendment of by-laws to split CEO & Chairman positions
Intel INTC:
10/29/14 10Q & 10/14/14 8K re: 3rd Qtr ended 9/27/14
9/26/14 8K re: Intel investment in & collaboration with Tsinghua Unigroup
11/5/14 8K re: underwriting contract with JPMorgan
10/28/14 10Q & 2 8Ks (10/20) re: 3Qtr ended 9/30/14
10/20/14 8K re: closing of Lenovo's purchase of IBM's x86 server business
10/20/14 8K re: sale of IBM's global comm'l semiconductor tech business to Globalfoundries
7/29/14 10Q & 7/18/14 8K & 7/17/14 8K re: qtr. ended 6/30/14
7/29/14 8K re: election of CEO of JNJ Alex Gorsky & Peter R. Voser to BoD
JPMorgan Chase JPM:
11/3/14 & 2 8Ks (10/14) re: 3Qtr ended 9/30/14
10/22/14 8K re: sale of 2.2% notes due '19
10/2/14 8K re: cyberattack
10/2/14 8K re: adjustment of warrant price
9/19/14 8K re: redemption of subord. notes
9/12/14 8K re: cyberattack vs. JPM
9/10/14 8K re: closing of public offering of $3 bil sub. notes due'24
8/4/14 10Q & 7/15/14 8K & 7/15/14 8K re: qtr. ended 6/30/14
Johnson & Johnson JNJ:
10/30/14 10Q & 10/14/14 8K re: 3Qtr ended 9/28/14
10/2/14 8K re: agreement to purchase Alios Biopharma
8/1/14 10Q & 7/15/14 8K re: Qtr ended 6/29/14
McDonald's MCD:
11/3/14 10Q & 10/21/14 8K re: 3Qtr ended 9/30/14
9/22/14 8K re: raising quarterly div. by 5% to 85 cents payable 12/15 to record holders 12/1
9/9/14 8K re: global sales decreased 3.7% in Aug.
8/27/14 8K re: salary increase of Pres. of Asia, Mid E. & Africa
8/22/14 8K re: election of Make Andres as Pres. - USA replacing Jeff Stratton eff. 10/15
8/11/14 8K re: global sales decreased 2.5% in July
8/4/14 & 7/22/14 & 7/18/14 8K re: qtr. ended 6/30/14
Merck MRK:
10/27/14 8K re: 3Qtr results
10/15/14 8K re: issuance of notes
10/2/14 8K re: completion of sale of Consumer Care Business to Bayer for 414.2 bil
9/29/14 8K re: 2Q results
Microsoft MSFT:
10/23/14 10Q & 10/23/14 8K re: 1Qtr ended 9/30/14
10/21/14 & 10/20/14 & 10/20/14 Proxy re: Annual Shareholder Mtg at 12/3/14 at 8 am at Meydenbauer ctr., Bellevue, WA
9/17/14 8K election of Teri List-Stoll & Charles W. Scharf (CEO of Visa) to Board eff 10/1 & increase of Board to 12 & retirement from Board of Dave Marquadt & Dina Dublon
8/19/14 8K re: dividend increase to 31 cents up 11% payable 12/111 to holders on 11/20
Nike NKE:
10/7/14 10Q & 9/30/14 8K & 9/25/14 8K re: 1Qtr ended 8/31/14
9/23/14 8K re: results of annual shareholders meeting
Sec. 14A Proxy re: Annual Meeting of Shareholders to be held 9/18/14 at Tiger Woods Conf. center, Beaverton, Or.
Pfizer PFE:
11/6/14 10Q & 10/28/14 8K re: 3Qtr ended 9/28/14
8/7/14 10Q for qtr ended 6/29/14
Procter & Gamble PG:
11/4/14 8K re: closing of sale of floating rate notes due '64
11/3/14 8K re: sale of notes
11/3/14 re: Argentina regulatory problems re: taxes
10/24/14 10Q & 2 8Ks (10/24) 1Qtr ended 9/30/14
10/20/14 8K re: voting results of 10/14 Annual Mtg of Shareholders
10/14/14 8K re: dividend of 64 cents payable 11/17 to record holders on 10/24/14
8/29/14 Proxy re: 10/14/14 Annual Meeting of Shareholders at 9 a.m. at Duke Energy Convention Ctr. Cincinnati,Oh
8/8/14 10K for yr. ended 6/30/14
8/1/14 2 8Ks re: 4Q results
10/30/14 10Q & 10/23/14 8K re: 3Qtr ended 9/30/14
8/12/14 8K re: election of Sandra Barbour to Board
8/8/14 8K re: $2.25 bil 5 yr. revolving credit agreement with JPMorgan
7/31/14 10Q & 7/24/14 re: qtr. ended 6/30/14
Travelers TRV:
10/21/14 10Q & 10/21/14 8K re: 3Qtr ended 9/30/14
9/10/14 2 8Ks re: realignment of 2 of 3 business segments
8/11/14 8K re: amendment to bylaws re: timing of shareholder proposals
United Technologies UTX:
10/24/14 10Q & 10/21/14 8K re: 3Qtr ended 9/30/14
UnitedHealth Group UNH:
10/16/14 8K re: 3Qtr results
9/12/14 8K re: FD disclosures re: presentation at Merrill Global Healthcare Conf. London 9/17
9/5/14 8K re: FD disclosure re: presentation at Morgan Stanley Healthcare Conf. NYC 9/9
8/4/14 & 8/1/14 8K & 7/17 8K re: qtr. ended 6/30/14
Verizon Communications Inc. VZ:
10/28/14 10Q & 10/21/14 8K re: 3Qtr ended 9/30/14
9/11/14 8K re: strong customer growth
9/4/14 8K/A committee Board assignments for Dir. Shellye L. Archambeau
8/20/14 8K re: results of exchange offer of Verizon/Alltel securities
8/6/14 2 8Ks re: terms of exchange offer re: Alltel
Visa V:
10/29/14 8K re: 4Qtr & full year ended 9/30/14 results
10/22/14 8K re: 1/28/15 Annual Stockholders Mtg & dividend of 48 cents payable 12/2 to record holders on 11/14/14
9/24/14 8K re: new conversion rate of Class B Common
9/11/14 8K re: deposit of $450 mil in litigation escrow account
WalMart WMT:
10/30/14 8K re: Closing of Walmart Seiyu stores in Japan
10/17/14 8K re: issuance of notes
9/29/14 8K re: election to Bd. of Instagram CEO & Founder Kevin Systrom
9/5/14 10Q & 8/14/14 8K re: results for qtr ended 7/31/14


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Cheap bus tickets to Rotorua Airport
- Auckland Airport
Rotorua Airport7:50 AM11:40 AM18 Feb12Go Asia
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Search Events
The Great Gatsby at Gatsby's Mansion
Step into the Roaring Twenties as F. Scott Fitzgerald's The Great Gatsby is bought to life in this immersive show at Gatsby's Mansion in London.
Put on your best 1920s-inspired outfit and join the fun as you're led through Jay Gatsby's store into one of his infamous parties in this interactive performance.
Venue Details & Map
Gatsby's Mansion
- Address
Gatsby's Mansion
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Heckbarley is a fabulous holiday cottage offering self-catering accommodation for up to 11 guests in the picturesque village of Ennerdale Bridge. It is located close to Ennerdale Lake in the beautiful setting of of the Lake District National Park, it is a great place in which to explore the fells and lakes. Perfect for family or group holidays.
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Location: Ennerdale, Cleator, Cumbria, CA23 3AR
Tariff: From £300 - £1300 Per Week
Rooms: 1 to 11
Wi-Fi Parking Pets Allowed
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Several healings were reported when the church was being built and Mont Saint-Michel still remains a Catholic pilgrimage site. The role of Saint Michael as protector and guardian has also led to the design of statues that depict him and the construction of Churches and monasteries at specific locations. Because most monastic islands lie close ...
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