Question

Find the inclusive range, the sample standard deviation, and the sample variance of each of the following scores:

a. 5, 7, 9, 11

b. 0.3, 0.5, 0.6, 0.9

c. 6.1, 7.3, 4.5, 3.8

d. 435, 456, 423, 546, 465

Answer 1

a) range = 11 - 5 = 6

Mean = (5 + 7 + 9 + 11)/4 = 8

Variance = ((5 - 8) ^2 + (7 - 8)^2 + (9 - 8)^2 + (11 - 8)^2)/3 = 6.667

Standard deviation = = 2.582

b) range = 0.9 - 0.3 = 0.6

Mean = (0.3 + 0.5 + 0.6 + 0.9)/4 = 0.575

Variance = ((0.3 - 0.575)^2 + (0.5 - 0.575)^2 + (0.6 - 0.575)^2 + (0.9 - 0.575)^2)/3 = 0.0625

Standard deviation = = 0.25

c) range = 6.1 - 3.8 = 2.3

Mean = (6.1 + 7.3 + 4.5 + 3.8)/4 = 5.425

Variance = ((6.1 - 5.425)^2 + (7.3 - 5.425)^2 + (4.5 - 5.425)^2 + (3.8 - 5.425)^2)/3 = 2.4892

Standard deviation = = 1.5777

d) range = 546 - 423 = 123

Mean = (435 + 456 + 423 + 546 + 465)/5 = 465

Variance = ((435 - 465)^2 + (456 - 465)^2 + (423 - 465)^2 + (546 - 465)^2 + (465 - 465)^2)/4 = 2326.5

Standard deviation = = 48.2338