Question

calculate ss, variance, and standard deviation for the following sample of $n = 5$ scores: 2, 9, 5, 5, 9.

Explanation:

Step1: Calculate the mean

First, find the sum of the scores: $2 + 9+5 + 5+9=30$. The mean $\bar{x}=\frac{30}{5}=6$.

Step2: Calculate the squared - deviations

For $x_1 = 2$: $(2 - 6)^2=(-4)^2 = 16$.
For $x_2 = 9$: $(9 - 6)^2=3^2 = 9$.
For $x_3 = 5$: $(5 - 6)^2=(-1)^2 = 1$.
For $x_4 = 5$: $(5 - 6)^2=(-1)^2 = 1$.
For $x_5 = 9$: $(9 - 6)^2=3^2 = 9$.

Step3: Calculate the sum of squares (SS)

$SS=16 + 9+1+1+9=36$.

Step4: Calculate the variance

The variance $s^2=\frac{SS}{n - 1}=\frac{36}{5 - 1}=\frac{36}{4}=9$.

Step5: Calculate the standard deviation

The standard deviation $s=\sqrt{s^2}=\sqrt{9}=3$.

Answer:

$SS = 36$, Variance $= 9$, Standard Deviation $= 3$