Question

Below are the jersey numbers of 11 players randomly selected from a football team. Find the​ range, variance, and standard deviation for the given sample data. What do the results tell​ us?

53   98   58   69   16   65   32   95   59   15   44

Answer 1

x	(x-mu)	(x-mu)^2
15	-39.9	1592.7
16	-38.9	1513.9
32	-22.9	524.8
44	-10.9	119.0
53	-1.9	3.6
58	3.1	9.6
59	4.1	16.7
65	10.1	101.8
69	14.1	198.6
95	40.1	1607.3
98	43.1	1856.8
Sum = 604		Sum = 7544.90

(3) We know that standard deviation is given by:

s.d. = sqrt(variance)

s.d. = sqrt(685.9)

s.d = 26.189.

Interpretation: The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. Here, s.d = 26.189..