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Interpreting Histograms (Edexcel IGCSE Maths A (Modular))

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Roger B

Written by: Roger B

Reviewed by: Dan Finlay

Edexcel Maths A (Modular): Higher Unit 1Edexcel Maths A: HigherCambridge (CIE) Maths: Extended

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Interpreting Histograms

How do I interpret a histogram?

  • It is important to remember that the frequency density (y-) axis does not tell us frequency

    • The area of the bar is equal to the frequency

      • table row frequency equals cell frequency space density cross times class space width end cell end table

  • Note that a very simple histogram may have equal class widths

    • In this case the y-axis may be labelled 'frequency' instead of 'frequency density'

    • If 'frequency' is on the y-axis, then you can use the heights of the bars to directly determine the frequencies

  • You may be asked to estimate the frequency of part of a bar/class interval within a histogram

    • Find the area of the bar for the part of the interval required

    • Once area is known, frequency can be found as above

  • You can use histograms for two data sets to compare the data distributions

    • but only if they have the same class intervals and the same frequency density scales

Examiner Tips and Tricks

  • The frequency density axis will not always be labelled

    • Look carefully at the scale, it is unlikely to be 1 unit to 1 square

Worked Example

The table below and the corresponding histogram show the weight, in kg, of some newborn bottlenose dolphins.

Weight
w kg

Frequency

4 ≤ w < 8

4

8 ≤ w < 10

16

10 ≤ w < 12

19

12 ≤ w < 15

12

15 ≤ w < 30

A partially complete histogram for the data in the question.

(a) Use the histogram to complete the table.

The frequency for the 15 ≤ w < 30 class interval is missing

The bar for that class interval on the histogram has a

  • height (frequency density) of 0.6

  • width of 30-15 = 15

Rearrange frequency space density equals fraction numerator frequency over denominator class space width end fractionto get

frequency equals frequency space density cross times class space width

frequency equals 0.6 cross times 15 equals 9

Weight
w kg

Frequency

4 ≤ w < 8

4

8 ≤ w < 10

16

10 ≤ w < 12

19

12 ≤ w < 15

12

15 ≤ w < 30

9

(b) Use the table to complete the histogram.

The bar for the 4 ≤ w < 8 class interval is missing

That class interval has a

  • frequency of 16

  • width of 10-8 = 2

Use frequency space density equals fraction numerator frequency over denominator class space width end fraction to find the frequency density

frequency space density equals 16 over 2 equals 8

Draw a bar with that height on the histogram, between 8 and 10 on the horizontal axis

A completed histogram for the data in the question.

(c) Estimate the number of dolphins whose weight is greater than 13 kg.

We know from part a) that there are 9 dolphins in the 15 ≤ w < 30 class interval
So we need to estimate the number of dolphins that are in the interval 13 ≤ w < 15

For 13 ≤ w < 15, the histogram shows that

  • the frequency density is 4

  • the width is 15-13 = 2

The histogram from the question with the bar between 13 and 15 highlighted.

Now use frequency equals frequency space density cross times class space width to estimate the number of dolphins in the 13 ≤ w < 15 interval
(Note that using the histogram in this way is actually a form of linear interpolation)

frequency equals 4 cross times 2 equals 8

This is only an estimate because we don't actually know that dolphins are evenly distributed across the entire 12 ≤ w < 15 class interval

Now the total number of dolphins with a weight greater than 13 kg can be estimated

8 plus 9 equals 17

There are approximately 17 dolphins with a weight greater than 13 kg

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    Author
    Reviewer
    Roger B

    Author: Roger B

    Expertise: Maths

    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

    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.