Question

A district manager rewards sales teams based on overall sales generated in a month. The data for earnings are shown in the table, where Low represents the lowest sales and High represents the highest sales generated by a single sales team member.
Team Low High Range Mean Median IQR σ
Team X 275 2780 2505 1440.6 1432 837.7 716.8 Team Y 925 1850 925 1376.3 1371 443.3 259.8
Team Z 2250 3900 1650 3006.3 2943 542 505.9 Part A: If the manager wants to award the sales team that has the most consistent earnings among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)

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

Answer 1

A.) The first one is Team Y because of the range.
B.) Is team z because the mean is more and larger than the others. 
Hope this helps. If you need more help or explanation let me know. :)

Answer 2

Answer with explanation:

Part A: We check range to determine the consistency of data because range  is used to measure the spread of the data.

Less range signifies the more consistency of the data .

From the given table , Team Y has the least range , it means Team Y has the most consistent earnings among its team members.

Thus, It should choose Team Y because of its lower range.

Part B: We check mean values to determine the average earnings beacuse mean is synonym to average..

From the given table, Team Z has the largest mean value.

It means , it should choose Team Z to award them with the highest average earnings because it has the highest mean value.