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A customer-support company tracked the average number of cases resolved per day by six regional teams during four consecutive quarters. The graph shows the average for each team in Quarters 1 through 4.
Using the drop-down menus, complete each statement most accurately based on the information provided.
The four quarterly averages have the greatest variance for .
If, for each team, the increase or decrease in the average from Quarter 2 to Quarter 3 had been repeated from Quarter 3 to Quarter 4, the smallest Quarter 4 average would have been for .
A customer-support company tracked the average number of cases resolved per day by six regional teams during four consecutive quarters. The graph shows the average for each team in Quarters 1 through 4.
Using the drop-down menus, complete each statement most accurately based on the information provided.
The four quarterly averages have the greatest variance for .
If, for each team, the increase or decrease in the average from Quarter 2 to Quarter 3 had been repeated from Quarter 3 to Quarter 4, the smallest Quarter 4 average would have been for .
Official Solution:
Drop-down 1:
Variance measures how spread out a set of values is around its mean.
From the graph, Flint has the greatest range between its highest and lowest quarterly averages, and its four points are clearly more spread out than those of the other teams.
Therefore, the four quarterly averages have the greatest variance for Flint.
Drop-down 2:
For each team, imagine that the line from Quarter 2 to Quarter 3 continues from Quarter 3 to Quarter 4 with the same slope. Since the quarters are equally spaced, this means repeating the same increase or decrease.
From the graph, Elm decreases from about 80 in Quarter 2 to about 70 in Quarter 3. Continuing with the same slope would place its hypothetical Quarter 4 average at about 60.
Flint also decreases from Quarter 2 to Quarter 3, but continuing that decrease would place its hypothetical Quarter 4 average above Elm’s. The other teams would also have higher hypothetical Quarter 4 averages.
Therefore, the smallest hypothetical Quarter 4 average would have been for Elm.
1. Clearly, Flint has the highest deviation from its mean. So, obviously, Flint will have the highest variance. Had the least variance been asked, it would've been Atlas. 2. To find the smallest Quarter 4 average, let's rule out the absolute confirmed ones that are higher: a. Beacon showed a positive slope from Q2 to Q3, so it will be positive from Q3 to Q4. b. Cedar was slightly decreasing; following the same trend, it would still have been above 70. c. Delta shows a similar positive trend as Beacon, so it is out. Between Elm and Flint, Elm decreased from roughly 80 to 70 from Q2 to Q3, so the same trend in Q4 means 60. Now, Flint decreased from 92 to 78 (which is a 14-point drop); following the same trend, 78-14 gives 64 in Q4. Hence, Elm has the lowest average in Q4.