Question

The following are the amounts contributed by 6 friends contributed fortrekking.$2, $9, $8, $7, $9, $7Find the standard deviation.

Answer 1

The given data are

2, 9, 8, 7, 9, 7

To find the standard deviation we will find the mean at first

`Mean=(sum)/(no.)`

The sum = 2 + 9 + 8 + 7 + 9 + 7 = 42

The no. = 6, then

`\begin{gathered} Mean=(42)/(6) \\ \\ Mean=7 \end{gathered}`

Then we will square the difference between each number and the mean

`\begin{gathered} (2-7)^2=25 \\ (9-7)^2=4 \\ (8-7)^2=1 \\ (7-7)^2=0 \\ (9-7)^2=4 \\ (7-7)^2=0 \end{gathered}`

Add all the answers

`\sum_^(x-M)^2=25+4+1+0+4+0=34`

Divide it by the no. and find the square root

`\begin{gathered} \sigma=\sqrt{(\sum_^(x-M)^2)/(N)} \\ \\ \sigma=\sqrt{(34)/(6)} \\ \\ \sigma=2.380476143 \end{gathered}`

The standard deviation is about 2.38 to the nearest hundredth