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Maths

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Maths

Histograms and frequency density - Higher

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Histograms and frequency density

​​In a nutshell

Histograms are like bar charts but with varying bar widths. Rather than height, it is the area of each bar that shows frequency.



Drawing a histogram

​​Definition

Class width

The difference between the start and end value of the class.

In order to draw a histogram from a frequency table, another quantity needs to be worked out: frequency density - the height of each bar shows this frequency density.

frequency density=frequency÷class width \text{frequency density} = \text{frequency} \div \text{class width }​​


procedure

​​1.

Add a frequency density column to table.

2.

Draw and label your axes:

  • the y-axis should have the frequency density.
  • the x-axis should have the thing being measured.

3.

Draw your bars - remember the width of the bars should correspond to the class widths.


Example 1

Below is a frequency table showing the ages of students in a school production. Draw the histogram.


Age (aa)

Frequency

6<a106<a\le10​​

44​​

10<a1210<a\le12​​

55​​

12<a1312<a\le13​​

22​​

13<a1813<a\le18​​

11​​


Add the frequency density column.

Frequency density (frequency density=frequency÷class width \text{frequency density} = \text{frequency} \div \text{class width })

4÷4=14\div4=1​​

5÷2=2.55\div2=2.5​​
2÷1=22\div1=2​​
1÷5=0.21\div5=0.2​​


Now following the steps and drawing the histogram gives:

Maths; Statistics; KS4 Year 10; Histograms and frequency density - Higher


Frequently Asked Questions (FAQ)

FAQs

  • Question: How do I draw a histogram?

    Answer: To draw a histogram: 1. Add a frequency density column. 2. Draw and label your axes: - The y-axis should have the frequency density. - The x-axis should have the thing being measured. 3. Draw your bars - remember the width of the bars should correspond to the class widths.

  • Question: What is the equation for frequency density?

    Answer: Frequency density = frequency ÷ class width. The height of each bar shows frequency density.

  • Question: What is the class width?

    Answer: The class width is the difference between the start and end value of the class.

  • Question: What is the difference between a bar chart and a histogram?

    Answer: Histograms are like bar charts but with varying bar widths. Rather than height, it is the area of each bar that shows frequency.

Theory

Exercises

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