Question

Given the following data on the ages of 75 persons in years. Calculate the first four central moments. Age 09.5–14.5 ,14.5–19.5 , 19.5–24.5 , 24.5–29.5 , 29.5–34.5 ,34.5–39.5, 39.5–44.5 , 44.5–49.5

Number of persons: 3,6,8,12,8,6,3,2 Total 75

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Answer 1

$c_i-middles\,\,of\,\,the\,\,intervals\\w_i-frequencies\\\mu =\frac{\sum{c_iw_i}}{\sum{w_i}}=27\\Central\,\,moments:\\\mu _1=\mu -\mu =0\\\mu _2=\frac{\sum{\left( c_i-\mu \right) ^2w_i}}{\sum{w_i}}=78.125\\\mu _3=\frac{\sum{\left( c_i-\mu \right) ^3w_i}}{\sum{w_i}}=333.333\\\mu _4=\frac{\sum{\left( c_i-\mu \right) ^4w_i}}{\sum{w_i}}=15703.13$