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


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)

Respuesta :

merlynthewhizz
A) The most consistent data shows a low range as it means the values of the data are not varied so much. Team Y has the lowest range of 125. 

B) The highest average earnings are Team X, with the highest value of X. We choose the mean as to measure the highest average earnings because the calculation of mean would have included every value in the data set
nobillionaireNobley
Gven that a district manager rewards sales teams based on overall sales generated in a month and that 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    1970       2970         1200        2571.9         2684         426.3   313.8
Team Y      250         375           125          315.8           311           59        37.8
Team Z      950       1900           950        1529.9         1473         276      180.7

Part A: A data set, say X, is said to be more consistent than another data set, say Y, if data set X is less spread out than data set Y.
The range is used to determine the spread of the data. The range is calculated by subtracting the lowest data value from the highest data value.
From the data presented in the table, above, Team Y has the smallest spread (range) compaired to the other teams and hence is the most consistent team.

Therefore, if the manager wants to award the sales team that has the most consistent earnings among its team members, he should choose Team Y.


Part B: Average also known as mean is a measure of central tendency which measure the center of a given dataset be taking the sum of the dataset and dividing the result by the number of the dataset.

From the data presented in the table above, the team with the highest mean is Team X with a mean of 2571.9 compared to a mean of 1529.9 of Team Z and 315.8 of Team Y.

Therefore, if the manager wants to award the sales team with the highest average earnings, it should choose Team X.

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