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 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 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.

Answer 1

To compare the datasets based on variability, we can look at the standard deviation, which measures the amount of variation or dispersion from the mean. A lower standard deviation indicates that the data points are closer to the mean, which means less variation.

Here are 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

To find the dataset with the least variation, we look for the dataset with the smallest standard deviation:

- Dataset A: 1.9
- Dataset B: 1.41
- Dataset C: 1.2
- **Dataset D: 1.14** (the least variation)

Thus, **Dataset D** has the least variation among the datasets, with a standard deviation of 1.14.

**Interpretation**: Even though Dataset D has the highest mean (48), it has the lowest standard deviation, indicating that its data points are relatively close to the mean compared to the other datasets. Thus, if we want to select the dataset with the least variation, we would choose Dataset D.