Question

Find the sum of squares of the deviations from the mean of a series of ACT scores listed below. 17, 27, 16, 26, 14

Answer 1

Statistics

We have the following dataset:

x={17,27,16,26,14}

First, we calculate the mean value:

$x=\frac{17+27+16+26+14}{5}=\frac{100}{5}=20$

Now we find the deviations from the mean:

17-20 = -3

27-20= 7

16-20 = -4

26-20= 6

14-20 = -6

Now we find the squares of each deviation and sum all of them:

$\begin{gathered} S=(-3)^2+7^2+(-4)^2+6^2+(-6)^2 \\ S=9+49+16+36+36=146 \end{gathered}$