Question

The numbers of prisoners executed by the state since 1977 for the top 12 states are listed below. Find the range, variance, and standard deviation of the data.

Answer 1

Range:

Range = Highest value – Lowest value

From the given data set, the highest value is 355 and lowest value is 22.

 

Therefore, the range is,

Range = 355 – 22

            = 333

 

Variance:

The formula for variance is given below:

s2 = Σ(X – X̅)2/n - 1

 

The mean is obtained below:

X	X – X̅	(X – X̅)
355	281.917	79477.19
94	20.917	437.52
34	-39.083	1527.48
79	5.917	35.01
27	-46.083	2123.64
66	-7.083	50.17
39	-34.083	1161.65
39	-34.083	1161.65
27	-46.083	2123.64
22	-51.083	2609.47
60	-13.083	171.16
35	-38.083	1450.31
X̅ = 73.083		Σ(X – X̅)2 = 92,328.92

 

Therefore, the variance is,

s2 = 92,328.92/(12 – 1)

     = 92,328.92/11

     = 8,393.5

 

Standard deviation.

The formula for standard deviation is given below:

s = √s2

   = √Σ(X – X̅)2/(n – 1)

 

Therefore, the standard deviation

s = 8393.538

s = 91.6

The variance is 8,393.5

 

Standard deviation is 91.6.