Cumulative Frequency

Key Facts and Exam Tips

• Cumulative frequency is like a running total. It is the total frequency at the end of each class interval in a frequency table.
  
• Examination questions may give you a grouped frequency table and ask you to find the cumulative frequency in the next column. Alternatively, the table may already give cumulative frequencies that you will be required to plot.
  
• Plot the end of the class interval, reading from the horizontal axis, against the cumulative frequency, which is always read from the vertical axis.
  
• Take care to read the scales given accurately. It is usually helpful to work out what each small square of graph paper represents. Remember that the axes may well have different scales, so you need to check both the vertical axis and horizontal axis.
  
• The median value is the 'middle' of the set of data. If there are n values altogether then the median is the (n+1)/2 th value. In many cases it is accurate enough to simply find n/2 for the middle of the data. Read across from this value on the cumulative frequency axis to the curve and down onto the horizontal axis. The median is the value read from the horizontal axis.
  
• The lower quartile is one-quarter of the way into the data. For n values it is the (n+1)/4 th value. Again, finding n/4 gives a good approximation, unless n is very small. Read across to the graph and down to the horizontal axis to find the lower quartile.
  
• The upper quartile is three-quarters of the way into the data. Find 3(n+1)/4 or 3n/4 and read the value from the graph as above.
  
• Remember when performing the above steps that n is the total number of values. This figure is the same as the last entry in the cumulative frequency table. It is not necessarily the same as the top of the scale on the cumulative frequency axis, so you can't just divide the axis into halves and quarters.
  
• The range is the difference between the highest and lowest values in the data. It is a measure of the spread of the data.
  
• The interquartile range is the difference between the upper and lower quartiles and it tells you the spread of the middle 50% of the data.
  
• A box plot shows the median, quartiles and upper and lower values for a set of data.