Histograms (DP IB Analysis & Approaches (AA)): Revision Note

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Histograms

What is a (frequency) histogram?

  • A frequency histogram clearly shows the frequency of class intervals

    • The classes will have equal class intervals

    • The frequency will be on the y-axis

    • The bar for a class interval will begin at the lower boundary and end at the upper boundary

  • A frequency histogram is similar to a bar chart

    • A bar chart is used for qualitative or discrete data and has gaps between the bars

    • A frequency histogram is used for continuous data and has no gaps between bars

What are (frequency) histograms useful for?

  • They show the modal class clearly

  • They show the shape of the distribution

    • It is important the class intervals are of equal width

  • They can show whether the variable can be modelled by a normal distribution

    • If the shape is symmetrical and bell-shaped

Worked Example

The table below and its corresponding histogram show the mass, in kg, of some new born bottlenose dolphins.

Mass, m kg

Frequency

4 less or equal than m less than 8

4

8 less or equal than m less than 12

15

12 less or equal than m less than 16

19

16 less or equal than m less than 20

10

20 less or equal than m less than 24

6

a) Draw a frequency histogram to represent the data.

4-1-6-ib-ai-aa-sl-histogram-a-we-solution

b) Write down the modal class.

4-1-6-ib-ai-aa-sl-histogram-b-we-solution

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Dan Finlay

Author: Dan Finlay

Expertise: Maths Subject 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.