This table presents the mean and standard deviation for three datasets, showing variations in their central values and speed. Dataset Mean Standard Deviation 1 78 1.23 2 81 1.42 3 83 1.19 Which has the highest variability? (1 point) Responses Dataset 1 Dataset 1 Dataset 2 Dataset 2 Dataset 3

Answer 1

To determine which dataset has the highest variability, we can calculate the coefficient of variation (CV) for each dataset. The coefficient of variation is calculated as the standard deviation divided by the mean, often expressed as a percentage.

Here's how we calculate it for each dataset:

1. Dataset 1:

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

2. Dataset 2:

   • Mean = 81
   • Standard Deviation = 1.42
   • CV = (1.42 / 81) × 100 ≈ 1.754%

3. Dataset 3:

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

Now, comparing the coefficients of variation:

• Dataset 1: ≈ 1.577%
• Dataset 2: ≈ 1.754%
• Dataset 3: ≈ 1.432%

Dataset 2 has the highest coefficient of variation, indicating it has the highest variability.

So the answer is Dataset 2.