Question

1. calculate $ss, sigma^{2}$ and $sigma$ for the following population of $n = 4$ scores: 0, 6, 6, 8.

Explanation:

Step1: Calculate the mean ($\mu$)

$\mu=\frac{0 + 6+6 + 8}{4}=\frac{20}{4}=5$

Step2: Calculate the sum - of - squares (SS)

$SS=\sum(X-\mu)^2=(0 - 5)^2+(6 - 5)^2+(6 - 5)^2+(8 - 5)^2$
$=(-5)^2+1^2+1^2+3^2=25 + 1+1+9=36$

Step3: Calculate the variance ($\sigma^{2}$)

$\sigma^{2}=\frac{SS}{N}=\frac{36}{4}=9$

Step4: Calculate the standard deviation ($\sigma$)

$\sigma=\sqrt{\sigma^{2}}=\sqrt{9}=3$

Answer:

$SS = 36$, $\sigma^{2}=9$, $\sigma = 3$