Question

In a data set consisting of 10 values
$x_1,x_2,....,x_{10}$ such that $-10\le x_i\le 10$ with mean 0, what can be the maximum standard deviation?

• A. 10
• B. 100
• C. 81
• D. Insufficient data

Answer 1

The correct option is A 10

$Variance=\frac{\sum _{}^{}{\left(x_i-\overline{x}\right)}^2}{N}\mathrm{Since}\overline{x}=0\mathrm{Variance}=\frac{\sum _{}^{}{\left(x_i\right)}^2}{N}=\frac{\sum _{}^{}{\left(x_i\right)}^2}{10}$

The maximum ${x_i}^2$ can be ${10}^2$. Let us see if each ${x_i}^2$ can be made ${10}^2$ then we would really get the maximum value of variance that is 100 and SD will be 10. If we choose the data set to be{-10,-10,-10,-10,-10,10,10,10,10,10} then the mean will be 0.
Hence maximum SD is 10.