Given:
the following population of N = 8
scores: 1, 3, 1, 10, 1, 0, 1, 3
We will find the variance and standard deviation
We will use the following formula:
[tex]variance=s^2=\frac{\sum(x-\mu)^2}{N}[/tex]First, we will find the mean (μ):
[tex]μ=\frac{sum}{N}=\frac{1+3+1+10+1+0+3+1}{8}=\frac{20}{8}=2.5[/tex]Construct the following table:
Data (x - μ) (x-μ)²
1 (1-2.5) 2.25
3 (3-2.5) 0.25
1 (1-2.5) 2.25
10 (10-2.5) 56.25
1 (1-2.5) 2.25
0 (0-2.5) 6.25
1 (1-2.5) 2.25
3 (3-2.5) 0.25
Now, find the sum of (x-μ)²
[tex]\sum(x-\mu)^2=2.25+0.25+2.25+56.25+2.25+6.25+2.25+0.25=72[/tex]So, the variance will be:
[tex]variance=s^2=\frac{72}{8}=9[/tex]And the standard deviation will be:
[tex]standard\text{ }deviation=\sigma=\sqrt{s^2}=\sqrt{9}=3[/tex]So, the answer will be:
Variance = 9
The standard deviation = 3
