Question

consider the women’s 100-yd dash (and the subsequent 100-m dash) in the olympics since records have been kept. determine the best way to combine all data and depict the data. choose the correct answer below. a. a stem and leaf plot would be the best way to show all of the data grouped by race times. b. a scatterplot would show the relationship between the 100-yd dash and the 100-m dash. c. a histogram would show all of the data by comparing each year. the units of distance would not matter. d. a line graph would be the best way to show all of the data over time, but some measurements would have to be converted to display the 100-yd and 100-m on the same graph.

Explanation:

To determine the best graph for women’s 100 - yd and 100 - m dash Olympic records:

• Option A: Stem - and - leaf plots are for showing the distribution of a single dataset, not for comparing two related datasets (100 - yd and 100 - m dash times), so A is incorrect.
• Option B: A scatter plot is used to show the relationship between two quantitative variables. Here, we can plot 100 - yd dash times on one axis and 100 - m dash times on the other to see their relationship, which is appropriate for these two related race time datasets.
• Option C: A histogram is for showing the distribution of a single variable (e.g., frequency of times in a range for one race), not for comparing two different race datasets, so C is incorrect.
• Option D: A line graph is for showing change over time for a variable. While we could show data over time, the main goal here is to combine and depict the relationship between 100 - yd and 100 - m dash times, not just show change over time. Also, the unit conversion issue is a complication, and a scatter plot is better for showing the relationship between the two variables. So D is incorrect.

Answer:

B. A scatterplot would show the relationship between the 100 - yd dash and the 100 - m dash.