What is the variance of the following set of numbers?: {40, 56, 59, 60, 60, 62, 65, 69, 75, 84}

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Answer 1 · 2018-05-15T12:20:27

#123.8#

First of all, find the average, defined as the sum of all items divided by the number of items:

#\mu = 1/N\sum_{i=1}^N x_i#

so, in your case,

#\mu = \frac{40+56+59+60+60+62+65+69+75+84}{10} = \frac{630}{10}=63#

Then, you must compute the squared distance of each item from the average:

#40 \to (40 - 63)^2 = 529#

#56 \to (56 - 63)^2 = 49#

#59 \to (59 - 63)^2 = 16#

#60 \to (60 - 63)^2 = 9#

#62 \to (62 - 63)^2 = 1#

#65 \to (65 - 63)^2 = 4#

#69 \to (69 - 63)^2 = 36 #

#75 \to (75 - 63)^2 = 144#

#84 \to (84 - 63)^2 = 441#

The variance is defined as the sum of the squared distances, divided by the number of items:

#sigma^2 = \frac{529+49+16+9+9+1+4+36+144+441}{10} = \frac{1238}{10} = 123.8#