Question

Please help!!!

Tammy and Wyatt are sales associates at the same used car dealership. Their supervisor is planning to promote the employee with the best sales numbers, on average. The box plots in the picture show their sales, in thousands of dollars, for the past two weeks.

Who should get the promotion, and why?
a.) Wyatt should get the promotion. His data is more evenly distributed, so his sales are more consistent.
b.) Wyatt should get the promotion because he had the highest sales in a single day.
c.) Tammy should get the promotion because her lowest value is higher than Wyatt’s lowest value.
d.) Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.

Answer 1

Answer: D) Tammy should get the promotion. She has a higher median and a smaller IQR, so her sales are better on average.

It is true that Wyatt has some sales values that are higher than Tammy's max (Eg: Wyatt's max is 28 thousand while Tammy's max is just a bit short of this). Though Tammy's median, as marked by the vertical line inside her box and whisker plot, is larger than Wyatt's median. Also, the box portion for Tammy's plot is shorter indicating a smaller IQR. Smaller IQRs tell the reader that the sales figures are more concentrated in a certain area and they are more consistent and on target. Wyatt's IQR is larger so his sales are more spread out and not as predictable. Furthermore, Tammy's Q1 value is higher than Wyatt's Q1 value. The same can be said about the min value for Tammy. All of these pieces of evidence show that her sales are better on average, which is why she should get the promotion.