Calculate sample- mean, variance & standard deviation for data set: 2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 2, 0, 5, 1, 4, 2, 0, 5, 1, 4, 2, 1, 0.

Question

Calculate the sample mean, sample variance, and sample standard deviation for the following data set:
2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 2, 0, 5, 1, 4, 2, 0, 5, 1, 4, 2, 1, 0.

Answer 1

2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 2, 0, 5, 1, 4, 2, 0, 5, 1, 4, 2, 1, 0

This is your sample data. There are 27 samples.

 

The sample mean is the mean of this data. Add them together and divide by 27.

54/27=2

 

The variance is the (sum of all (x - the mean)^2) divided by the number of samples

2-2, 2-2, 0-2, 5-2, 1-2, 4-2, 1-2, 3-2, 0-2, 0-2, 1-2, 4-2, 4-2, 0-2, 2-2, 0-2, 5-2, 1-2, 4-2, 2-2, 0-2, 5-2, 1-2, 4-2, 2-2,  1-2, 0-2

 

0, 0, -2, 3, -1, 2, -1, 1, -2, -2, -1, 2, 2, -2, 0, -2, 3, -1, 2, 0, -2, 3, -1, 2, 0, -1, -2

 

(0, 0, -2, 3, -1, 2, -1, 1, -2, -2, -1, 2, 2, -2, 0, -2, 3, -1, 2, 0, -2, 3, -1, 2, 0, -1, -2)^2

 

0, 0, 4, 9, 1, 4, 1, 1, 4, 4, 1, 4, 4, 4, 0, 4, 9, 1, 4, 0, 4, 9, 1, 4, 0, 1, 4

 

Add them toget her =82

 

Variance = 82/27 = 3.037

 

Standard deviation is the square root of the variance.

Sqrt(3.037) = 1.7427