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

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 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.

Answer 1

To determine which dataset has the least variation, you should focus on the standard deviation. The standard deviation measures how spread out the values in a dataset are; a lower standard deviation indicates that the data points are closer to the mean, suggesting less variation.

Here's a summary of the standard deviations for each dataset:

- Dataset A: Standard Deviation = 1.9
- Dataset B: Standard Deviation = 1.41
- Dataset C: Standard Deviation = 1.2
- Dataset D: Standard Deviation = 1.14

From this information, we can see that Dataset D has the lowest standard deviation (1.14), indicating it has the least variation among the datasets.

**Interpretation**:
- Dataset D exhibits the least variation in its values, as indicated by its lower standard deviation compared to the other datasets. Despite having the highest mean (48), the data points in Dataset D are more closely clustered around the mean than those in Datasets A, B, and C.

Thus, based on the standard deviations given, Dataset D is the one with the least variation.