Compute SS variance and standard deviation for the following population. Scores: 1,3,9,3

Answer 1

Population Samples: 1,3,9,3

Population Mean = 4

Deviations: -3, -1, 5, -1

Sum of Squares = 36

No. of Samples = 4

SS Population Variance = 36/4 = 9

Population Standard Deviation = Square Root of SS Population Variance = Square Root of 9 = 3.0

Answer 2

The easiest way is to let your calculator do this task for you but I have the feeling you are supposed to do it manually.

To do this manually, you will use the following calculation for the variance. Remember this formula is only for a POPULATION (not for a sample):

Then the standard deviation is the square root of that variance.

First find the mean (μ) by adding the numbers and dividing by the number of numbers (4):

1 + 3 + 9 + 3 = 16 and 16/4 = 4 so μ=4.

Then set up a table like this:

x x - μ (x - μ)²

1 -3 9

3 -1 1

9 5 25

3 -1 1

Then add up the last column: 9 + 1 + 25 + 1 = 36

Now divide that sum by the number in the population (4): 36/4 = 9 which is the variance

To find the standard deviation, take the square root: √9 = 3