Why does the formula for calculating the sample variance, s- , involve squaring

Question

Why does the formula for calculating the sample variance, s- , involve squaring the difference between each value and the mean? n-1 Choose the correct answer below O A. If the differences were not squared, then the formula would be calculating the sample standard deviation instead of the variance. O B. The formula involves squaring the differences so that the square root can be taken when the sample standard deviation is calculated ° C· lf the differences were not squared, then the sum of all deviations from the mean would always be zero since the positive deviations are balanced by the negative deviations. The formula involves squaring the differences so that the units on the sample variance will be the same as the units on the original data. D.

Explanation / Answer

Here right answer is C

C. If the difference were not squared, then the sum of all deviation from the mean would always be zero since the positive deviation are balanced by the negative deviation.

I.e. sum of (Xi - Xbar) is always zero so option C is correct

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