Calculate SS, variance, and standard deviation for the sample of n = 4 scores: 7, 4, 2, 1 (The computational formula works well with these scores)

Question

Calculate SS, variance, and standard deviation for the sample of n = 4 scores: 7, 4, 2, 1. (The computational formula works well with these scores)

Answer 1

Hi Margaret,

 

We have 4 scores: 7, 4, 2, 1

 

Even though you haven't been asked for it, we need to calculate the mean.

 

7+4+2+1

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     4

 

= 14/4 = 3.5

 

 

 

Next, let's calculate the SS (sum of the squares)

For each score the square of the difference between the score and the mean score is:

(7-3.5)² = 12.25

(4-3.5)² = 0.25

(2-3.5)² = 2.25

(1-3.5)² = 6.25

Now add them to get the SS

12.25+0.25+2.25+6.25 = 21.00 = SS

 

Variance = SS/(n-1) = 21/(4-1) = 21/3 = 7

 

Standard deviation = √variance = √7