Question

Saras test scores in mathematics were 64, 80, 88, 78, 60, 92, 84, 76, 86, 78, 72 and 90 mean : 79median: 79mode: 78calculate the standard deviation and round to the hundredths

Answer 1

The sample standar deviation formula is given by

$\sigma=\sqrt[]{\frac{\Sigma(x_j-\mu)}{n-1}}$

where

$\begin{gathered} x_j\text{ are the values} \\ \mu\text{ is the mean} \\ n\text{ in the number of elements in the sample} \end{gathered}$

In our case, the mean is 79 and there are 12 elements (n=12). By substituting the values into the formula, we have

$\sigma=\sqrt[]{\frac{(64-79)+(80-79)+(88-79)+(78-79)+(60-79)+(92-69)+(84-69)+(76-69)+(86-69)+(78-69)+(72-69)+(90-69)}{12-1}}$

This is equal to,

$\sigma=\sqrt[]{\frac{70}{11}}$

then, the sample standar deviation is equal to 2.52