Question

1. calculate $ss, sigma^{2}$, and $sigma$ for the following population of $n = 5$ scores: 6, 0, 4, 2, 3.

Explanation:

Step1: Calculate the mean ($\mu$)

$\mu=\frac{6 + 0+4+2+3}{5}=\frac{15}{5}=3$

Step2: Calculate the squared - deviation for each score

For $x_1 = 6$: $(6 - 3)^2=9$
For $x_2 = 0$: $(0 - 3)^2 = 9$
For $x_3 = 4$: $(4 - 3)^2=1$
For $x_4 = 2$: $(2 - 3)^2 = 1$
For $x_5 = 3$: $(3 - 3)^2=0$

Step3: Calculate the sum of squares (SS)

$SS=9 + 9+1+1+0=20$

Step4: Calculate the population variance ($\sigma^{2}$)

$\sigma^{2}=\frac{SS}{N}=\frac{20}{5}=4$

Step5: Calculate the population standard deviation ($\sigma$)

$\sigma=\sqrt{\sigma^{2}}=\sqrt{4}=2$

Answer:

$SS = 20$, $\sigma^{2}=4$, $\sigma = 2$