Question

1. a sample of $n = 10$ scores has a sample mean of $m = 25$ and a sample standard deviation of $s = 4$. what are the values of $sum x$ and $ss$?

Explanation:

Step1: Recall the formula for the sample mean

The formula for the sample mean $M=\frac{\sum X}{n}$. We can re - arrange it to find $\sum X$. Given $n = 10$ and $M=25$, we have $\sum X=n\times M$.
$\sum X=10\times25 = 250$

Step2: Recall the formula for the sample standard deviation and sum of squares

The formula for the sample standard deviation $s=\sqrt{\frac{SS}{n - 1}}$, where $SS$ is the sum of squares. Squaring both sides gives $s^{2}=\frac{SS}{n - 1}$, and then we can re - arrange to get $SS=s^{2}(n - 1)$. Given $s = 4$ and $n=10$, first find $s^{2}=4^{2}=16$, and then $SS=16\times(10 - 1)$.
$SS=16\times9=144$

Answer:

$\sum X = 250$, $SS = 144$