Question

The leaders of two youth sports teams randomly select five members of each team and record their ages, as shown.

• Team A 16, 13, 12, 16, 13

• Team B: 10, 13, 16, 16, 10

Which statement appropriately compares the ages of the team members?

Members of Team A and members of Team B are likely the same average (mean) age.

Members of Team A are likely younger, and they have less variability in their ages.

Members of Team A are likely older, and they have more variability in their ages.

D Members of Team A are likely older, and they have less variability in their ages.

Answer 1

Members of Team A are likely older, and they have less variability in their ages.

Explanation:

To solve this question, we need to find the mean and the standard deviation for each team.

Team A 16, 13, 12, 16, 13

The mean is:

`M = (16 + 13 + 12 + 16 + 13)/(5) = 14`

The standard deviation is:

`S = \sqrt{((16-14)^2 + (13-14)^2 + (12-14)^2 + (16-14)^2 + (13-14)^2)/(5)} = 1.67`

Team B: 10, 13, 16, 16, 10

The mean is:

`M = (10 + 13 + 16 + 16 + 10)/(5) = 13`

The standard deviation is:

`S = \sqrt{((10-13)^2 + (13-13)^2 + (16-13)^2 + (16-13)^2 + (10-13)^2)/(5) = 13} = 2.68`

Which statement appropriately compares the ages of the team members?

Sample of team A has higher mean age, which means that they are likely older. They also have a smaller standard deviation, so they likely have less variability in their ages.