Question

the results of a school’s drama club fundraiser are displayed in the double line graph shown. 4. reasoning which product had more variability in their sales? would your answer change if wrapping paper sales on day 4 were $200? explain. 5. if the drama club wanted to compare overall wrapping paper sales of the 7th graders to the 8th graders, would a back - to - back stem - and - leaf plot work better than a double line graph to display the data? explain.

Explanation:

Step1: Analyze variability from graph

Observe the range of sales for each product. For gift - cards, the minimum sales seem to be around $25$ and the maximum around $175$. The range is $175 - 25=150$. For wrapping paper, the minimum is around $50$ and the maximum is $250$. The range is $250 - 50 = 200$. Since $200>150$, wrapping paper has more variability.

Step2: Consider changed value

If wrapping paper sales on day 4 were $200$, the new range for wrapping paper is $200 - 50=150$. Now, the ranges for both gift - cards and wrapping paper are the same ($150$), so the answer would change.

Step3: Evaluate data - display for 7th and 8th graders

A back - to - back stem - and - leaf plot is better for comparing two sets of data when you want to see the distribution of values and compare individual data points. A double line graph is better for showing trends over time. Since we want to compare overall sales (not trends over time) of 7th and 8th graders, a back - to - back stem - and - leaf plot would work better.

Answer:

1. Wrapping paper had more variability initially. The answer would change if wrapping paper sales on day 4 were $200$ because the ranges of gift - card and wrapping paper sales would be equal.
2. A back - to - back stem - and - leaf plot would work better because it is better for comparing distributions of two sets of data rather than showing trends (which a double line graph is for).