Inequalities of Levin-Ste\v{c}kin, Clausing and Chebyshev revisited
  We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality . 
Alfred Witkowski
math.CA