Question

What is the standard deviation of the following data set rounded to the nearest tenth?

Answer 1

The standard deviation is 6.3.

We first find the mean by adding all of the values and dividing by the number of data points:
(534+524+539+530+537+522)/6 = 3186/6 = 531

We now use the following formula to find the standard deviation:
$\sigma=\sqrt{\frac{(x_1-\mu)^2+(x_2-\mu)^2+...}{n}} \\ \\=\sqrt{\frac{(534-531)^2+(524-531)^2+(539-531)^2+(530-531)^2+(537-531)^2+(522-531)^2}{6}} \\ \\=\sqrt{\frac{3^2+(-7)^2+8^2+(-1)^2+6^2+(-9)^2}{6}} =\sqrt{\frac{9+49+64+1+36+81}{6}}=\sqrt{\frac{240}{6}} \\ \\=\sqrt{40}\approx 6.3$