Comparing Univariate Graphs (College Board AP® Statistics)

Study Guide

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Comparing univariate graphs

What is a univariate graph?

  • In statistics, univariate means there is one variable

    • This variable may be categorical or quantitative

  • A univariate graph shows data for one variable

    • Types of univariate graphs include

      • bar charts

      • histograms

      • dotplots

      • stem-and-leaf plots

      • cumulative graphs

  • A scatterplot is not a univariate graph

    • because it shows two variables

How do I compare univariate graphs?

  • You may be given two graphs for two different data sets with the same context

  • You need to compare four different things:

    • The centers of the data

      • either visually or using means, medians and modes

    • The spread (variability) of the data

      • either visually or using ranges, interquartile ranges and standard deviations

    • The shape of the distributions

      • the skew (or any symmetry)

    • Any unusual features of the graphs, in particular any

      • outliers

      • gaps

      • clusters

      • or multiple peaks (unimodal, bimodal or uniform)

Examiner Tips and Tricks

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.

Examiner Tips and Tricks

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

Worked Example

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 bar chart comparing the number of books bought by males and females.

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

Answer:

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)

Comparing the centers of the data, the number of books bought by male customers has two consecutive modes on Thursday and Friday whereas the number of books bought by female customers has one mode on Thursday
This suggests that Thursday, in particular, was a popular day

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

Comparing the shapes of the distributions, the number of books bought by male customers has a strong negative (left) skew whereas the number of books bought by female customers has a weak negative (left) skew
This suggests that the number of books bought by males and females generally increased over the week

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) which form slight clusters around Tuesday and around Thursday

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

Answer:

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

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Mark Curtis

Author: Mark Curtis

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.