GCSEMathsOCRHigherRevision Notes12. StatisticsHistogramsDrawing Histograms

Drawing Histograms (OCR GCSE Maths): Revision Note

Exam code: J560

Roger B

Written by: Roger B

Reviewed by: Dan Finlay

Updated on

OCR Maths: HigherWJEC Eduqas Maths: HigherAQA Maths: HigherEdexcel Maths: Higher

Drawing histograms

What is a histogram?

  • A histogram looks similar to a bar chart, but there are important differences

  • Bar charts are used for discrete (and sometimes non-numerical) data

    • In a bar chart, the height (or length) of a bar determines the frequency

    • There are usually gaps between the bars

  • Histograms are used with continuous data, grouped into class intervals (usually of unequal width)

    • In a histogram, the area of a bar determines the frequency

      • This means it is difficult to tell anything simply from looking at a histogram

      • Some basic calculations will be needed for conclusions and comparisons to be made

    • There are no gaps between the bars

How do I draw a histogram?

  • Drawing a histogram first requires the calculation of the frequency densities for each class interval (group)

    • Use  table row cell frequency space density end cell equals cell fraction numerator frequency over denominator class space width end fraction end cell end table

    • Exam questions often ask you to finish an incomplete histogram, rather than start with a blank graph

  • Once the frequency densities are known, the bars (rectangles) for each class interval can be drawn

    • with widths being measured on the horizontal (x) axis

    • and the height of each bar (the frequency density) being measured on the vertical (y) axis

    • As the data is continuous, the bars will be touching

Examiner Tips and Tricks

  • Always work out and write down the frequency densities

    • It is easy to make errors and lose marks by going straight to the graph

    • Method marks may depend on showing you know to use frequency density rather than frequency

Worked Example

A histogram is shown below representing the distances achieved by some athletes throwing a javelin.

A partially completed histogram for distances of javelins thrown by athletes.

There are two classes missing from the histogram.  

These are:

Distance, x m

Frequency

60 less or equal than x less than 70

8

80 less or equal than x less than 100

2

 Add these to the histogram.

Before completing the histogram, remember to show clearly you've worked out the missing frequency densities

Distance, x m

Frequency

Class width

Frequency density

60 less or equal than x less than 70

8

70 - 60 = 10

8 ÷ 10 = 0.8

80 less or equal than x less than 100

2

100 - 80 = 20

2 ÷ 20 = 0.1

Now the bars can be drawn on the histogram
They should stretch along the x-axis from the start to the end of the class interval
The heights will be equal to the frequency densities

histogram worked example with missing bars drawn

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself
    Previous:Frequency DensityNext:Interpreting Histograms
    Author
    Reviewer
    Roger B

    Author: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

    Dan Finlay

    Reviewer: 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.