Cumulative frequency
- Cumulative frequency is a running total of the frequencies.
- Plot each cumulative frequency at the upper class boundary, then join the points with a smooth curve or straight lines. Start from the lower boundary of the first class at zero.
- The total frequency (n) is the last cumulative frequency.
Median, quartiles and percentiles
- For large grouped data, read estimates from the graph: the median at n ÷ 2, the lower quartile (LQ) at n ÷ 4 and the upper quartile (UQ) at 3n ÷ 4.
- The interquartile range (IQR) = UQ − LQ. It measures the spread of the middle 50% and isn't affected by extreme values.
- Percentiles split the data into 100 parts and deciles into 10. The 90th percentile is read at 90% of n.
- To find how many values are above a value, read the cumulative frequency at that value and subtract it from n.
Box plots
- A box plot shows the five-number summary: minimum, LQ, median, UQ and maximum. Outliers can be marked with a cross.
- Example: minimum 12, LQ 20, median 25, UQ 32, maximum 45. The IQR is 12 and the range is 33.
- When comparing box plots, compare an average (the median) and a measure of spread (the IQR), and write about what they mean in context.
Key terms
- Cumulative frequency
- A running total of the frequencies.
- Median
- The middle value when data is in order.
- Lower quartile
- The value one quarter of the way through ordered data.
- Upper quartile
- The value three quarters of the way through ordered data.
- Interquartile range
- Upper quartile minus lower quartile.
- Box plot
- A diagram showing the minimum, quartiles, median and maximum.
- Percentile
- A value below which a given percentage of the data falls.