Question

Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth. 23 20 14 35 28

Answer 1

The standard deviation for given sample is 7.97

Explanation:

We are given the following data set:

23, 20, 14, 35, 28

Formula:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(120)/(5) = 24`

Sum of squares of differences = 1 + 16 + 100 + 121 + 16 = 254

`S.D = \sqrt{(254)/(4)} = 7.97`

The standard deviation for given sample is 7.97