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