Question

A professor records the time (in minutes) that it takes 16 students to complete an exam. Compute the SS, the variance, and the standard deviation assuming the 16 students constitute a population and assuming the 16 students constitute a sample. (Round your answers for variance and standard deviation to two decimal places.)

19 28 47 22
38 28 40 37
51 39 53 42
32 13 20 31
(a) the 16 students constitute a population
SS
variance
standard deviation min

(b) the 16 students constitute a sample
SS
variance
standard deviation

Answer 1

Explanation:

The formula for determining the sum of squares is expressed as

Σ(x - mean)²

n = 16

Mean = (19 + 28 + 47 + 22 + 38 + 28 + 40 + 37 + 51 + 39 + 53 + 42 + 32 + 13 + 20 + 31)/16 = 33.75

Σ(x - mean)² = (19 - 33.75)^2 + (28 - 33.75)^2 + (47 - 33.75)^2 + (22 - 33.75)^2 + (38 - 33.75)^2 + (28 - 33.75)^2 + (40 - 33.75)^2 + (37 - 33.75)^2 + (51 - 33.75)^2 + (39 - 33.75)^2 + (53 - 33.75)^2 + (42 - 33.75)^2 + (32 - 33.75)^2 + (13 - 33.75)^2 + (20 - 33.75)^2 + (31 - 33.75)^2

SS = 2059

Variance = Σ(x - mean)²/n

Variance = 2059/16 = 128.69

Standard deviation = √variance

Standard deviation = √128.6875

Standard deviation = 11.34