Cumulative frequency
- Cumulative frequency is a running total of the frequencies. Frequencies 4, 7, 9 and 5 give cumulative frequencies 4, 11, 20 and 25.
- Plot each cumulative frequency at the upper end of its group, and join the points with a smooth curve.
Reading the graph
- For n values, read the median at n ÷ 2, the lower quartile at n ÷ 4 and the upper quartile at 3n ÷ 4 on the cumulative frequency axis. Go across to the curve, then down.
- Interquartile range (IQR) = upper quartile − lower quartile. It measures the spread of the middle half of the data, and extreme values don't affect it.
- To find how many values are above a point, read up to the curve and subtract from the total.
Box plots
- A box plot shows five values: the minimum, lower quartile, median, upper quartile and maximum.
- For minimum 12, lower quartile 20, median 25, upper quartile 31 and maximum 40, the IQR is 11 and the range is 28.
Comparing distributions
- Compare an average (the median) and a spread (the IQR or range), and write each comparison in context.
- 'Class A's median is higher, so on average Class A did better. Class B's IQR is smaller, so Class B's marks were more consistent.'
Key terms
- Cumulative frequency
- A running total of the frequencies.
- Lower quartile
- The value a quarter of the way through the ordered data.
- Upper quartile
- The value three quarters of the way through the ordered data.
- Interquartile range
- Upper quartile − lower quartile: the spread of the middle half of the data.
- Box plot
- A diagram showing the minimum, quartiles, median and maximum.
- Distribution
- The way a set of data is spread out.