Question

calculate the ss, variance, and standard deviation for the population of n = 8 scores: 1, 3, 1, 10, 1, 0, 1, 3. the ss would be select . the variance would be select . the standard deviation select . *for these answers, they will all be whole numbers.

Explanation:

Step1: Calculate the mean ($\mu$)

The sum of the scores is $1 + 3+1 + 10+1+0+1+3=20$. The population size $N = 8$. So, $\mu=\frac{20}{8}=2.5$.

Step2: Calculate the squared - deviations and sum of squares (SS)

For $x_1 = 1$: $(1 - 2.5)^2=(-1.5)^2 = 2.25$
For $x_2 = 3$: $(3 - 2.5)^2=(0.5)^2 = 0.25$
For $x_3 = 1$: $(1 - 2.5)^2=(-1.5)^2 = 2.25$
For $x_4 = 10$: $(10 - 2.5)^2=(7.5)^2 = 56.25$
For $x_5 = 1$: $(1 - 2.5)^2=(-1.5)^2 = 2.25$
For $x_6 = 0$: $(0 - 2.5)^2=(-2.5)^2 = 6.25$
For $x_7 = 1$: $(1 - 2.5)^2=(-1.5)^2 = 2.25$
For $x_8 = 3$: $(3 - 2.5)^2=(0.5)^2 = 0.25$

$SS=\sum(x-\mu)^2=2.25+0.25 + 2.25+56.25+2.25+6.25+2.25+0.25 = 72$.

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

The formula for population variance is $\sigma^{2}=\frac{SS}{N}$. Since $SS = 72$ and $N = 8$, $\sigma^{2}=\frac{72}{8}=9$.

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

The standard deviation is the square - root of the variance. So, $\sigma=\sqrt{9}=3$.

Answer:

The SS would be 72
The variance would be 9
The standard deviation would be 3