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

User Gui Ferreira
by
2.9k points

1 Answer

14 votes
14 votes

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

User Jun Hsieh
by
2.9k points
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