Question

Calculate SS. variance, and standard deviation for thefollowing population of N = 8 scores: 1, 3, 1, 10, 1,0, 1, 3. (Note: The computational formula works wellwith these scores.)

Answer 1

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:

`variance=s^2=(\sum(x-\mu)^2)/(N)`

First, we will find the mean (μ):

`μ=(sum)/(N)=(1+3+1+10+1+0+3+1)/(8)=(20)/(8)=2.5`

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

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

So, the variance will be:

`variance=s^2=(72)/(8)=9`

And the standard deviation will be:

`standard\text{ }deviation=\sigma=√(s^2)=√(9)=3`

So, the answer will be:

Variance = 9

The standard deviation = 3