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 A 22 58 36 42.1 44 18.25 10.35
Team B 38 49 11 43.9 44.5 3.5   2.97
Team C 27 36 9 31.8 32 3.75     2.55


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.
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.

Answer 1

Given the table below where Low represents the fewest points scored and High represents the highest points scored by a single team member.

$\begin{center} \begin{tabular} {|c||c|c|c|c|c|c|c|} Team & Low & High & Range & Mean & Median & IQR & \sigma \\ [1ex] Team A & 22 & 58 & 36 & 42.1 & 44 & 18.25 & 10.35 \\ Team B & 38 & 49 & 11 & 43.9 & 44.5 & 3.5 & 2.97 \\ Team C & 27 & 36 & 9 & 31.8 & 32 & 3.75 & 2.55 \end{tabular} \end{center}$

PART A:
The range, the IQR (inter-quartile range) and the standard deviations are measures which are used to measure the spread of a data set.

A dataset is more consistent relative to another data set when the standard deviation is less than that of the other data set.

From the table, it can be seen that Team C has the least standard deviation.

Therefore, If the club wants to award the team that has the most consistent scoring among its team members, team C should be chosen.


PART B
The mean and the median is a measure of center of a data set.
The mean describes the average of a data set.

From the table, it can be seen that Team B has the highest average score.

Therefore, If the club wants to award the team with the highest average score, team B should be chosen.

Answer 2

Part A:

The smaller the standard deviation the more consistent a set of data is.

Team C has the smallest standard deviation of 2.55 so they are the most consistent team.

Part B:

The mean is the average , so the higher the mean the higher the average. Team B has the higher average.