Question

Compare and interpret the measures to select the data with the least variation.

Dataset Mean Standard Deviation
A 21 1.9
B 29 1.41
C 25 1.2
D 48 1.14


(1 point)
Responses

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

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

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

To determine which dataset has the least variation, we should focus on the standard deviation, as it measures the dispersion or spread of values in a dataset. A smaller standard deviation indicates that the data points are closer to the mean, hence less variation.

**Comparison of Datasets:**

- **Dataset A:** Mean = 21, Standard Deviation = 1.9
- **Dataset B:** Mean = 29, Standard Deviation = 1.41
- **Dataset C:** Mean = 25, Standard Deviation = 1.2
- **Dataset D:** Mean = 48, Standard Deviation = 1.14

**Analysis of Standard Deviation:**

- **Dataset A's** standard deviation of 1.9 is the largest among the datasets, indicating greater variation.
- **Dataset B's** standard deviation of 1.41 is smaller than A's but larger than C's and D's.
- **Dataset C's** standard deviation is 1.2, which is quite low and indicates less variation compared to both A and B.
- **Dataset D's** standard deviation of 1.14 is the smallest of all, indicating the least variation among the datasets.

**Conclusion:**
Dataset D has the least variation, with the smallest standard deviation (1.14), even though its mean (48) is higher than the other datasets. Thus, if the goal is to select the dataset with the least variation based on standard deviation, **Dataset D is the best choice**.