Question

Find the sum of the differences squared betweenthe data entries and the mean.*36, 12, 42, 36, 36, 12*Do not include commas in your answer.

Answer 1

we are asked to determine the sum squared of the difference between the means and each value. To do that we will determine the mean first. The mean is given by:

$m=\frac{\text{ sum of terms}}{\text{ number of terms}}$

Replacing we get:

$m=\frac{36+12+42+36+36+12}{6}$

Solving the operations:

$m=\frac{174}{6}=29$

Now we determine the difference between each value and the mean:

$\begin{gathered} 36-29=7 \\ 12-29=-17 \\ 42-29=13 \\ 36-29=7 \\ 36-29=7 \\ 12-29=-17 \end{gathered}$

Now we square each of the values:

$\begin{gathered} 7^2=49 \\ (-17)^2=289 \\ (13)^2=169^{} \\ 7^2=49 \\ 7^2=49 \\ (-17)^2=289 \end{gathered}$

Now we find the sum of each of the terms we found:

$49+289+169+49+49+289=894$

Therefore, the sum of the differences squared between the data and the mean is 894.