Comparing Univariate Graphs (College Board AP® Statistics): Study Guide

In the exam, always remember to:

• use numbers from each graph in your comparisons,

• explain clearly which part of the graph you are talking about,

• relate any numbers or calculations back to the context of the question.

If the graphs do not have any unusual features, you should still write "no unusual features" to show the reader that you have checked for these.

The number of books bought during the opening week of a new bookshop is shown below. The shopkeeper wants to investigate shopping patterns between male and female customers.

(a) Compare the number of books bought by male and female customers during the opening week.

(b) Give one reason as to why the shopkeeper should not use the data shown to predict future shopping patterns.

Answer:

(a)

You need to compare:

• the centers of the data (either a mean, median or mode)

• the spread of the data (either a range, interquartile range or standard deviation)

• the shape of the distributions (skew, symmetry)

• and any unusual features (outliers, gaps, clusters, multiple peaks)

Calculate the mean for both males and females

Males: books per day

Females: books per day

Comparing the centers of the data, the average number of books per day for males is 12.8 which is smaller than the average number of books per day for females, which is 13.4

This suggests that on average, females bought more books

Comparing the spread of the data, the number of books bought by male customers has a range of 15 - 10 = 5 whereas the number of books bought by female customers has a range of 16 - 12 = 4, which is lower than that of male customers
This suggests that male customers have a greater variability in the number of books bought

The trend suggests that males buy more books as the week progresses

Comparing any unusual features, neither graph has any outliers or gaps
The number of books bought by male customers is always either increasing or staying the same, rising to a peak that spans both Thursday and Friday
The number of books bought by female customers has two peaks (bimodal) that form slight clusters around Tuesday and around Thursday

(b)

Reread the sentences at the beginning of the question

This data is for the opening week of the bookshop only

State that this is unrepresentative of a normal week

Give a specific real life example

The data shown is for the opening week of the bookshop, so it is unlikely to be representative of a normal week

Over time, the number of books bought may increase as the bookshop becomes more popular, or decrease if the customers lose interest

The number of goals scored per game by a soccer team throughout the soccer season is recorded. The results from the last season and the results from the current season are shown in the boxplots below. Compare the performance of the team last season with the performance of the team this season.

Answer:

You need to compare

• a measure of the centers of the data sets (the medians)

• the spread of the data (either the range or the interquartile range)

• the shape of the distributions (skew or symmetry)

• and any unusual features (e.g. outliers)

The median of goals scored per game last season is 3 goals per game
This is less than the median of goals scored per game this season, 4 goals per game
So, on average, the number of goals scored per game has increased
This suggests the team has improved

The interquartile range of goals scored per game last season is 4 − 1 = 3 goals
This is less than the interquartile range of goals scored per game this season, 8 − 2 = 6 goals
So, the number of goals scored per game this season is more spread out compared to last season
This suggests the team was playing more consistently last season than this season

For last season, the median is closer to the third quartile, giving a negative (left) skew of goals scored per game
This season, the median is closer to the first quartile, giving a positive (right) skew of goals scored per game

There were no outliers or unusual features last season and there are no outliers or unusual features this season

This suggests that the team's performance is better in the current season compared to the last season