Cumulative frequency diagrams
Cumulative frequency (Extended)
- The cumulative frequency is a running total of the frequencies.
- Plot it against the upper end of each class, then join the points with a smooth curve.
Practice
Cumulative frequency is:
Each point adds the next class frequency to the total so far.
Practice
Cumulative frequency is plotted against the upper end of each class.
Always plot the running total at the top boundary of the class.
Reading the curve
- Median: read across at half the total, then down.
- Quartiles: at one quarter and three quarters of the total.
- A percentile: e.g. the $90$th percentile is at $90\%$ of the total.
Practice
A cumulative frequency curve has total 80. At what cumulative frequency do you read the median?
The median is at half the total: 80 ÷ 2 = 40.
You've got it
Key idea
- cumulative frequency = running total, plotted at each class's upper end
- read the median at half the total; quartiles at ¼ and ¾
- across to the curve, then straight down to the value