<u>ANSWER: </u>
Standard deviation of 2, 4, 7, 8, 9 is 2.6
<u>SOLUTION:
</u>
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}}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B%5CSigma%28X%20i-%5Cmu%29%5E%202%7D%7Bn%7D%7D)
Where,
is element of data set
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}}](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7Bs%20u%20m%20o%20f%20%5Ctext%20%7B%20observations%20%7D%7D%7B%5Ctext%20%7Bnumber%20of%20observations%7D%7D)
![\begin{array}{l}{=\frac{2+4+7+8+9}{5}} \\\\ {=\frac{30}{5}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%3D%5Cfrac%7B2%2B4%2B7%2B8%2B9%7D%7B5%7D%7D%20%5C%5C%5C%5C%20%7B%3D%5Cfrac%7B30%7D%7B5%7D%7D%5Cend%7Barray%7D)
= 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}}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B%282-6%29%5E2%2B%284-6%29%5E2%2B%287-6%29%5E2%2B%288-6%29%5E2%2B%289-6%29%5E2%7D%7B5%7D%7D)
![\sigma=\sqrt{\frac{(-4)^2+(-2)^2+(1)^2+(2)^2+(3)^2}{5}}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B%28-4%29%5E2%2B%28-2%29%5E2%2B%281%29%5E2%2B%282%29%5E2%2B%283%29%5E2%7D%7B5%7D%7D)
![\begin{array}{l}{\sigma=\sqrt{\frac{16+4+1+4+9}{5}}} \\\\ {\sigma=\sqrt{\frac{34}{5}}} \\\\ {\sigma=\sqrt{6.8}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Csigma%3D%5Csqrt%7B%5Cfrac%7B16%2B4%2B1%2B4%2B9%7D%7B5%7D%7D%7D%20%5C%5C%5C%5C%20%7B%5Csigma%3D%5Csqrt%7B%5Cfrac%7B34%7D%7B5%7D%7D%7D%20%5C%5C%5C%5C%20%7B%5Csigma%3D%5Csqrt%7B6.8%7D%7D%5Cend%7Barray%7D)
So, the standard deviation is 2.607 approximately.
When rounded to nearest tenth answer is 2.6