Histograms (Cambridge (CIE) A Level Maths): Revision Note

Histograms

What is a histogram?

• A histogram is similar to a bar chart but with some key differences

  • A histogram is for displaying grouped continuous data whereas a bar chart is for discrete or qualitative data

  • There will never be any gaps between the bars of adjacent groups in a histogram

  • Whilst in a bar chart the frequency is read from the height of the bar, in a histogram the height of the bar is the frequency density

• On a histogram frequency density is plotted on the y – axis

  • This allows a histogram to be plotted for unequal class intervals

  • It is particularly useful if data is spread out at either or both ends

• The area of each bar on a histogram will be proportional to the frequency in that class

How do I draw a histogram?

• Step 1.  Always check that there are no gaps between the upper boundary of a class and the lower boundary of the next class

  • If there are gaps you will need to close them by changing the boundaries before carrying out any calculations

    • Consider whether the values are rounded or truncated before closing the gaps

• Step 2.  Find the class width of each group by subtracting the lower boundary from the upper boundary

• Step 3.  Calculate the frequency density for each group using the formula:

• Step 4.  The histogram will be drawn with the data values on the x – axis and frequency density on the y – axis

  • Remember that the scale on both axes must be even, although the class widths may be uneven

    • Both axes should be clearly labelled and units included on the x – axis

  • Most often, the bars will have different widths

How do we interpret a histogram?

• It is important to remember that the y – axis does not tell us the frequency of each bar in the histogram

• The frequency of a class is found by
  

  • 

• You may be asked to find the frequency of part of a bar within a histogram

  • Find the area of that section of the bar using any information you have already found out