How it works

A cumulative frequency diagram is drawn by plotting the running total of frequencies against the upper class boundary and joining points with a smooth curve. From this, the median, lower quartile and upper quartile can be estimated, which are then used to construct a box plot showing the minimum, lower quartile, median, upper quartile and maximum, along with the interquartile range.

The method

1. 1.Calculate the running total (cumulative frequency) for each class
2. 2.Plot cumulative frequency against the upper class boundary
3. 3.Draw a smooth curve or join points to make the cumulative frequency graph
4. 4.Read off values at n/4, n/2 and 3n/4 for quartiles and median

Worked example

Estimate the median from a cumulative frequency graph with total frequency 80.

1. Median position = 80/2 = 40
2. Read the value on the curve where cumulative frequency = 40

Worked example

Find the interquartile range if Q1 = 12 and Q3 = 27.

1. IQR = Q3 - Q1 = 27 - 12 = 15

Common mistakes

• Plotting cumulative frequency against the midpoint instead of the upper class boundary
• Reading quartiles at the wrong fraction of the total frequency
• Confusing range with interquartile range