Question

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

5,6,7,8,9,10,11,12,13,14

Answer 1

X	Mean, x̅	x-x̅	(x-x̅)²
5	9.5	-4.5	20.25
6	9.5	-3.5	12.25
7	9.5	-2.5	6.25
8	9.5	-1.5	2.25
9	9.5	-0.5	0.25
10	9.5	0.5	0.25
11	9.5	1.5	2.25
12	9.5	2.5	6.25
13	9.5	3.5	12.25
14	9.5	4.5	20.25

Range = Max - Min = 14 - 5 = 9

∑ x = 95

n = 10

Mean, x̅ = Ʃx/n = 95/10 = 9.5

∑(x-x̅)² = 82.5

Population Variance, σ² = Ʃ(x-x̅)²/(n) = 82.5/(10) = 8.25

Population Standard deviation, σ = √( Ʃ(x-x̅)²/(n) ) = √(82.5/(10)) = 2.87