Question

A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.


Team Low High Range Mean Median IQR σ
Team L 4 17 13 9.4 9 9.75 4.8
Team M 6 14 8 9.7 9.5 6.25 3.2
Team N 1 20 19 13 14.5 4.75 5.6


Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)

Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically. (5 points)

Answer 1

The team that should be awarded for consistent performance should be Team M. This is because the standard deviation of the team's players' scores is the lowest. Standard deviation is a measure of how much the individual data points vary from the average value, and for a consistent performance, this variation will be low.

The team with the highest average is Team N. The average is the same as the mean, and this is the highest for Team N, with a value of 13.

Answer 2

Answer:

Part A:  Team M has the most consistent scoring among its team members because they have the smallest range and their standard deviation is also the smallest, which indicates that the values are close together.

Part B: Team N has the highest average score because it has the highest mean and the highest median.