1. Cumulative frequency graphs
How to draw and use…..
Cumulative frequency graphs

2. Cumulative frequency is just…
A running total

3. Look at these tables Age, a (years) 3 9 17 10 5 Age, a (years) ≤ 12 3
Frequency
5 < a ≤ 12 3
12 < a ≤ 20 9
20 < a ≤ 30 17
30 < a ≤ 40 10
40 < a ≤ 60 5
Age, a
(years)
Cumulative
frequency
≤ 12 3
≤ 20
12 (3+9)
≤ 30
29 (3+9+17)
≤ 40
39 ( )
≤ 60
44 ( )

4. Once we have calculated the cumulative frequency
We don’t need the frequency any more.

5. We can use our results to draw a cumulative frequency curve
Age, a (years)
Cumulative
frequency
≤ 12 7
≤ 20 19
≤ 30 36
≤ 40 42
≤ 60 44
Along the ‘x’ axis
Up the ‘y’ axis

6. Plot the points 44 40 36 32 28 24 Cumulative 20 frequency 16 12 8 4
Cumulative
frequency
Age (years)

7. Draw the curve 44 40 36 32 28 24 Cumulative 20 frequency 16 12 8 4
Cumulative
frequency
Age (years)

8. Now draw in the median
Remember it is halfway up the cumulative frequency axis – in this case 22

9. Median…… 44 40 36 32 28 24 20 16 12 8 4 Cumulative frequency
Cumulative
frequency
halfway up
Read off here
Age (years)

10. The median is ……..
(about) 26.

11. Now for the lower quartile
Quarter of the way up the
Cumulative frequency axis

12. Lower Quartile 44 40 36 32 28 11 – quarter of 44 24 Cumulative 2016 12 8 4
11 – quarter of 44
Cumulative
frequency
Read off here
Age (years)

13. So the lower quartile is ….19

14. Three quarters of the way up the Cumulative frequency axis
Upper quartile
Three quarters of the way up the
Cumulative frequency axis

15. Upper quartile 33 – three quarters of 44 44 40 36 32 28 24 Cumulative20 16 12 8 4
Cumulative
frequency
Read off here
Age (years)

16. The upper quartile is …. 32

17. Upper quartile – lower quartile
Inter-Quartile range
Upper quartile – lower quartile

18. Upper quartile – lower quartile

19. Inter-quartile range =13

20. Try this one ….. 9 18 23 6 3 1 Salary (£) 10000 9 14000 27 18000 50
Frequency 9 18 23 6 3 1
Salary (£)
Cum. Freq.
10000 9
14000 27
18000 50
20000 56
24000 59
30000 60