Question

Compare and interpret the measures to select the data with the least variation.
This table provides a comparison of datasets with their mean and standard deviation.
Datase Mean Standard Deviation
A 21 1.9
B 29 1.41
C 25 1.2
D 48 1.14


(1 point)

Dataset B has a standard deviation of 1.41 and a mean of 29.

Dataset A has a standard deviation of 1.9 and a mean of 21.

Dataset C has a standard deviation of 1.2 and a mean of 25.

Dataset D has a standard deviation of 1.14 and a mean of 48.

Answer 1

Look at both absolute spread (standard deviation) and relative spread (coefficient of variation = SD/mean).

- Standard deviations: A 1.90, B 1.41, C 1.20, D 1.14. By absolute spread, D has the least variation.
- Coefficients of variation:
- A: 1.90/21 ≈ 0.0905 (9.05%)
- B: 1.41/29 ≈ 0.0486 (4.86%)
- C: 1.20/25 = 0.0480 (4.80%)
- D: 1.14/48 ≈ 0.0238 (2.38%)

By relative spread (CV) D also has the smallest variation. Conclusion: Dataset D shows the least variation both absolutely and relative to its mean.