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=(10(6750)-(240)^2)/(10(10-1))`
`\begin{gathered} S^2=(67500-57600)/(10(9)) \\ S^2=(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}`