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 σTeam X 1970 2970 1200 2571.9 2684 426.3 313.8Team Y 250 375 125 315.8 311 59 37.8Team Z 950 1900 950 1529.9 1473 276 180.7Part 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)

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04-08-2017
Mathematics

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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 σTeam X 1970 2970 1200 2571.9 2684 426.3 313.8Team Y 250 375 125 315.8 311 59 37.8Team Z 950 1900 950 1529.9 1473 276 180.7Part 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)

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merlynthewhizz merlynthewhizz · Answer 1 · 2017-08-11T00:14:00+02:00

PART A:

The most consistent team is the team who has the lowest range, IQR and standard deviation (σ). From the table, the team who has the lowest range, IQR and the standard deviation is team Y.

Lower range indicates a small range of data interval, meaning that there is no extremely low or high value on a set. It also means that most of the data values are repeated and therefore is more consistent.

PART B:

Average of a data can be shown by the value of the mean or median. From the table, we can see that team A has the highest mean and median. These values indicate the earning by sales each team member would have made.