Use the table to answer the question.

Question

Dataset Mean Standard Deviation
1 78 1.23
2 87
1.42

3 83 1.19
Which dataset has the least variability?

(1 point)
Dataset
has the lowest variability.

Answer 1

To determine which dataset has the least variability, we can evaluate the coefficient of variation (CV) for each dataset. The CV is calculated as the standard deviation divided by the mean, and is often expressed as a percentage. A lower CV indicates less variability relative to the mean.

Let's calculate the CV for each dataset:

1. Dataset 1:

   • Mean = 78
   • Standard Deviation = 1.23
   • CV = (1.23 / 78) * 100 ≈ 1.577%

2. Dataset 2:

   • Mean = 87
   • Standard Deviation = 1.42
   • CV = (1.42 / 87) * 100 ≈ 1.631%

3. Dataset 3:

   • Mean = 83
   • Standard Deviation = 1.19
   • CV = (1.19 / 83) * 100 ≈ 1.432%

Now we compare the CVs:

• Dataset 1: ≈ 1.577%
• Dataset 2: ≈ 1.631%
• Dataset 3: ≈ 1.432%

Dataset 3 has the lowest coefficient of variation, indicating that it has the least variability relative to its mean.

Thus, the answer is:

Dataset 3 has the lowest variability.