Histograms (CIE AS Maths: Probability & Statistics 1)

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