Question

ONLY find the variance and standard deviation not the mean or MAD27, 13,31,42,9,14,20,31,33,20

Answer 1

Step 1

State the formula for the variance

$S^2=\frac{n(\sum ^{}_{}x^2)-(\bar{\sum ^{}_{}x})^2}{n(n-1)}$$S^2=\frac{10(6750)-(240)^2}{10(10-1)}$$\begin{gathered} S^2=\frac{67500-57600}{10(9)} \\ S^2=\frac{9900}{90}=110 \end{gathered}$

Step 2

Find the standard deviation

$\begin{gathered} S=\sqrt[]{\text{Variance}} \\ S=\sqrt[]{110} \\ S=10.48808848 \\ S\approx10.49 \end{gathered}$