Question

Which of the following values is closest to the variance for the set of datashown below?

Answer 1

SOLUTION:

Case: Variance

Method:

The given values:

99,78,56,11,43,22,16,31,49,28,37,29,30,38,34

First we find the mean:

$\begin{gathered} \bar{x}=\frac{99+78+56+11+43+22+16+31+49+28+37+29+30+38+34}{15} \\ \bar{x}=\frac{601}{15} \\ \bar{x}=40.066667 \end{gathered}$

The variance is formula is given as:

$\begin{gathered} s^2=\sum_{n\mathop{=}0}^n\frac{(x-\bar{x})^2}{n-1} \\ s^2=\frac{SS}{15-1} \\ s^2=\frac{7506.9331}{14} \\ s^2=536.20952 \end{gathered}$

Final answer: Option (A)

Variance = 536.2