Question

What is the standard deviation of 5, 5, 9, 9, 9, 10, 5, 10, 10?​

Answer 1

Answer:

2.16 is the right answer

Answer 2

The standard deviation of the data set {5, 5, 9, 9, 9, 10, 5, 10, 10} is 2.2913.

Given,

The data set: 5, 5, 9, 9, 9, 10, 5, 10, 10.

To Find,

The standard deviation of the data set.

Solution,

The method of finding the standard deviation of the given data set is as follows -

We know that for a data set {x}, the standard deviation formula is $s=\sqrt{\frac{\sum x^2-\frac{(\sum x)^2}{n} }{n-1} }$, where n is the number of data present in the data set.

Let the data set be {x} = {5, 5, 9, 9, 9, 10, 5, 10, 10}.

So, {$x^{2}$} = {25, 25, 81, 81, 81, 100, 25, 100, 100}.

$\sum x=5+5+9+9+9+10+5+10+10=72$ and $\frac{(\sum x)^2}{n} =\frac{72^2}{9} =\frac{5184}{9}=576$, where n is the number of data in the data set.

Also, $\sum x^2=25+25+81+81+81+100+25+100+100=618$.

Let the standard deviation of the data set be s.

Then, $s^2=\frac{\sum x^2-\frac{(\sum x)^2}{n} }{n-1}=\frac{618-576}{9-1} =\frac{42}{8}=5.25$

⇒  $s=\sqrt{5.25} =2.2913$.

Hence, the standard deviation of the data set {5, 5, 9, 9, 9, 10, 5, 10, 10} is 2.2913.

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