Question

Compute the​ mean, range, and standard deviation for the data items in each of the three samples. Then describe one way in which the samples are alike and one way in which they are different.
Sample​ A: 25​, 29​, 33​, 37​, 41​, 45​, 49
Sample​ B: 25​, 27​, 29​, 37​, 45​, 47​, 49
Sample​ C: 25​, 25​, 25​, 37​, 49​, 49​, 49

Answer 1

I used the sample standard deviation (s = sqrt[Σ(x − x̄)²/(n−1)]). n = 7 for each sample.

Sample A: 25, 29, 33, 37, 41, 45, 49
- Mean x̄ = 37
- Range = 49 − 25 = 24
- s = sqrt(448/6) = sqrt(74.6667) ≈ 8.64

Sample B: 25, 27, 29, 37, 45, 47, 49
- Mean x̄ = 37
- Range = 49 − 25 = 24
- s = sqrt(616/6) = sqrt(102.6667) ≈ 10.13

Sample C: 25, 25, 25, 37, 49, 49, 49
- Mean x̄ = 37
- Range = 49 − 25 = 24
- s = sqrt(864/6) = sqrt(144) = 12.00

One way they are alike: all three have the same mean (37) and the same range (24).
One way they differ: their spreads differ — A is least variable (s ≈ 8.64), B is more variable (s ≈ 10.13), and C is most variable (s = 12); they also differ in shape (A is evenly spaced, B more mixed, C is clustered at the extremes).