Question

what is that standard deviation of the data set? round to the nearest tenth if needed.
2,4,7,8,9
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Answer 1

ANSWER:  

Standard deviation of 2, 4, 7, 8, 9 is 2.6

SOLUTION:

Given, data set is 2, 4, 7, 8, 9.

We know that, Standard deviation is given by

$\sigma=\sqrt{\frac{\Sigma(X i-\mu)^ 2}{n}}$

Where, $x_{i}$ is element of data set

$\mu$ is mean of data set

n is total number observations.

Now, mean is given by

$\mu=\frac{s u m o f \text { observations }}{\text {number of observations}}$

$\begin{array}{l}{=\frac{2+4+7+8+9}{5}} \\\\ {=\frac{30}{5}}\end{array}$

= 6

So, the mean of data set is 6.

Now, standard deviation,

$\sigma=\sqrt{\frac{(2-6)^2+(4-6)^2+(7-6)^2+(8-6)^2+(9-6)^2}{5}}$

$\sigma=\sqrt{\frac{(-4)^2+(-2)^2+(1)^2+(2)^2+(3)^2}{5}}$

$\begin{array}{l}{\sigma=\sqrt{\frac{16+4+1+4+9}{5}}} \\\\ {\sigma=\sqrt{\frac{34}{5}}} \\\\ {\sigma=\sqrt{6.8}}\end{array}$

So, the standard deviation is 2.607 approximately.

When rounded to nearest tenth answer is 2.6