Drawing Histograms

Drawing Histogramsvideo

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  $\begin{array}{rcl}\mathrm{frequency} \mathrm{density}& =& \frac{\mathrm{frequency}}{\mathrm{class} \mathrm{width}}\end{array}$

  • 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