Statistics Variability

Question

Calculate SS (sum of squares), variance, and standard deviation for the following Population of scores: 2,13,4,10,6.

Answer 1

First, find the mean of the population score.

μ = (2 + 13 + 4 + 10 + 6) / 5 = 35/5 = 7

Second, find variance by adding the sum of the difference of the individual point and the average and divide it by 5.

σ² = [(7 - 2)² + (7 - 13)² + (7 - 4)² + (7 - 10)² + (7 - 6)²] / 5 = (25 + 36 + 9 + 9 + 1)/5 = 80/5 = 16

Finally, square root the variance to get standard deviation.

σ = √16 = 4

Answer 2

Step 1: Calculate the mean of the sample.

mean = (2 + 13 + 4 + 10 + 6) / 5 = 7

Step 2: We need to square the difference of each data entry and the mean, and that will be the variance.

Variance: σ² = [(7 - 2)² + (7 - 13)² + (7 - 4)² + (7 - 10)² + (7 - 6)²] / 5 = (25 + 36 + 9 + 9 + 1)/5 = 16

Step 3: We calculate the square root of the Variance to get the standard deviation.

Standard Deviation: σ = √16 = 4