# Mean, Median, or Mode

Which one is my pencil?

Made by activity set in classroom

 However. in many instances. median. no conceptual meanings are associated with the algorithms or graphical methods. and mode are often presented as rote process. .Rationale  Determination of mean.

 Since one purpose of the activity is to have students find the mean and median lengths of pencils.  Use wooden pencils that have been sharpened to different lengths. and hand those to students for the activity. do not use mechanical pencils.Introducing the activity  Two factors should be considered before beginning this activity  Choice of pencils and class size. .

Penciling in the activity  Although the emphasis of the activity is on statistical concepts.  They record their values and those of the class in the table on activity sheet 1. they measure the actual length. it begins with estimation and measurement.  After students estimate the length of their pencil in centimetres. .

Discussion  Discuss with students how much their estimates differed from the actual measurements. . followed by probable reasons for the differences.

students should next measure two strips of paper that are equal to the length of their pencil. . then put their name and measurements on the strips for record-keeping purposes.  It is important for students to be able to easily identify their pencil/paper strips from everyone else’s. Since pencils cannot be folded or cut.

. then put your name and measurements on the strips for record-keeping purposes.Instruction for students  measure two strips of paper that are equal to the length of your pencil.

the other set will be used when finding median and mode. .  Collect the second paper ‘pencil’ from each student. organise them by length. and keep them in a separate pile.  The taped set should be used when finding the mean. and tape them together into one long strip. Take one paper ‘pencil’ from each student.

since it will take either four or five folds to get 16 or 32 equal pieces. respectively.  At this point.  See Activity sheet 2  The students simply fold the paper into the number of pieces equal to the number of observations (16 or 32). . lead an informal discussion of powers of 2.Physical determination of mean  Use the long taped strip and fold it numerous times to find the mean.

students should be able to see the equal pieces while being able to view all the original pencils lengths. . Once the paper folding is complete.  The length of each equal piece is the mean.

 Although this method enhances students’ understanding of mean. we feel it is important to explore the concept further. .  Students should compare their individual pencil length with the mean and explain why there are observations both above and below the mean.

 This allows students to see that the number of pencils above the mean as compared with those below the mean is roughly equivalent. we will use pencils that do not have lengths at one extreme or the other. we control the variability of the data set.  If our goal is to look at evenly distributed data. By using pencils that are sharpened to various lengths at the start. .

more pencil lengths on one side or the other of the mean will provide a physical example of skewed data. If our goal is to examine outliers.  Students then see that balance is more difficult to create. we will distribute pencils that are much shorter or much longer. .

Mean and mode  Students finish their exploration of the mean by using the mathematical formula. . which involves adding all the data and dividing by the number of pencils  See activity sheet 3.

ordered from smallest to largest. Students should place the other class set of strips alongside each other.  Unimodal or bimodal? . resembling a staircase.

finding the median requires using the middle two observations. we now find the median. With the strips remaining in order.  Quartiles? .  Since the data set will be an even number of observations.

and then contrast the effect of outliers on the median. .outliers  Use extremely short or long pencils to illustrate the effect of outliers on the mean.

so a number raised to the zero power is 1. . what will happen if only one pencil was in the data set?  Student discover that they cannot make a fold.The big payoff…  Ask the students.

. appreciating variability in real world: using language.  KC: Thinking (clarifying concepts). revisiting estimation and measurement and introducing power of 2. cooperation. working together. helping others. symbol and text.conclusion  Leaning intentions: using hands on physical models for familiar concepts.
The text passage describes an educational activity for teaching students about mean, median, and mode using physical models like pencils and paper strips. It outlines the steps of the activity, the rationale behind it, and how it helps students understand these statistical concepts through hands-on experience.
no_question

the passage does not contain any explicit mathematical questions or provide answers to such questions. instead, it provides a detailed description of an educational activity designed to teach statistical concepts.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Mean, Median, or Mode

Which one is my pencil?

Made by activity set in classroom

 However. in many instances. median. no conceptual meanings are associated with the algorithms or graphical methods. and mode are often presented as rote process. .Rationale  Determination of mean.

 Since one purpose of the activity is to have students find the mean and median lengths of pencils.  Use wooden pencils that have been sharpened to different lengths. and hand those to students for the activity. do not use mechanical pencils.Introducing the activity  Two factors should be considered before beginning this activity  Choice of pencils and class size. .

Penciling in the activity  Although the emphasis of the activity is on statistical concepts.  They record their values and those of the class in the table on activity sheet 1. they measure the actual length. it begins with estimation and measurement.  After students estimate the length of their pencil in centimetres. .

Discussion  Discuss with students how much their estimates differed from the actual measurements. . followed by probable reasons for the differences.

students should next measure two strips of paper that are equal to the length of their pencil. . then put their name and measurements on the strips for record-keeping purposes.  It is important for students to be able to easily identify their pencil/paper strips from everyone else’s. Since pencils cannot be folded or cut.

. then put your name and measurements on the strips for record-keeping purposes.Instruction for students  measure two strips of paper that are equal to the length of your pencil.

the other set will be used when finding median and mode. .  Collect the second paper ‘pencil’ from each student. organise them by length. and keep them in a separate pile.  The taped set should be used when finding the mean. and tape them together into one long strip. Take one paper ‘pencil’ from each student.

since it will take either four or five folds to get 16 or 32 equal pieces. respectively.  At this point.  See Activity sheet 2  The students simply fold the paper into the number of pieces equal to the number of observations (16 or 32). . lead an informal discussion of powers of 2.Physical determination of mean  Use the long taped strip and fold it numerous times to find the mean.

students should be able to see the equal pieces while being able to view all the original pencils lengths. . Once the paper folding is complete.  The length of each equal piece is the mean.

 Although this method enhances students’ understanding of mean. we feel it is important to explore the concept further. .  Students should compare their individual pencil length with the mean and explain why there are observations both above and below the mean.

 This allows students to see that the number of pencils above the mean as compared with those below the mean is roughly equivalent. we will use pencils that do not have lengths at one extreme or the other. we control the variability of the data set.  If our goal is to look at evenly distributed data. By using pencils that are sharpened to various lengths at the start. .

more pencil lengths on one side or the other of the mean will provide a physical example of skewed data. If our goal is to examine outliers.  Students then see that balance is more difficult to create. we will distribute pencils that are much shorter or much longer. .

Mean and mode  Students finish their exploration of the mean by using the mathematical formula. . which involves adding all the data and dividing by the number of pencils  See activity sheet 3.

ordered from smallest to largest. Students should place the other class set of strips alongside each other.  Unimodal or bimodal? . resembling a staircase.

finding the median requires using the middle two observations. we now find the median. With the strips remaining in order.  Quartiles? .  Since the data set will be an even number of observations.

and then contrast the effect of outliers on the median. .outliers  Use extremely short or long pencils to illustrate the effect of outliers on the mean.

so a number raised to the zero power is 1. . what will happen if only one pencil was in the data set?  Student discover that they cannot make a fold.The big payoff…  Ask the students.

. appreciating variability in real world: using language.  KC: Thinking (clarifying concepts). revisiting estimation and measurement and introducing power of 2. cooperation. working together. helping others. symbol and text.conclusion  Leaning intentions: using hands on physical models for familiar concepts.
user
The text passage describes an educational activity for teaching students about mean, median, and mode using physical models like pencils and paper strips. It outlines the steps of the activity, the rationale behind it, and how it helps students understand these statistical concepts through hands-on experience.

TYPE: NO_QUESTION

The passage does not contain any explicit mathematical questions or provide answers to such questions. Instead, it provides a detailed description of an educational activity designed to teach statistical concepts.