Question

Find the sum of squares of the deviations from the mean of a series of ACT scores listed below.31, 22, 24, 15, 23The sum of squares is(Type an integer or a decimal.)

Answer 1

Given the following scores below

`31,22,24,15,23`

To find the sum of squares of the deviations,

Firstly, we find the mean, the formula to find the mean of ungrouped data is

`\begin{gathered} \bar{x}=(\sum_X)/(n) \\ Where\text{ n is the number of terms} \end{gathered}`

Where n = 5

Substitute the given data into the formula to find the mean of ungrouped data

`\begin{gathered} \bar{x}=(31+22+24+15+23)/(5) \\ \bar{x}=(115)/(5)=23 \\ \bar{x}=23 \end{gathered}`

Secondly, we subtract the mean from each of the values given as shown below

`\begin{gathered} 31-23=8 \\ 22-23=-1 \\ 24-23=1 \\ 15-23=-8 \\ 23-23=0 \end{gathered}`

Then, to find the sum of squares of the deviations

We add the square of each of the deviations deduced above

`\begin{gathered} =(8)^2+(-1)^2+(1)^2+(-8)^2+(0)^2 \\ =64+1+1+64+0 \\ =130 \end{gathered}`

Hence, the sum of squares is 130