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

2. Cumulative frequency is just… A running total

3. Look at these tables Age, a (years) 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 ≤ 123 ≤ 2012 (3+9) ≤ 3029 (3+9+17) ≤ 4039 (3+9+17+10) ≤ 6044 (3+9+17+10+5)

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 ≤ 127 ≤ 2019 ≤ 3036 ≤ 4042 ≤ 6044 Along the ‘x’ axis Up the ‘y’ axis

6. Plot the points Cumulative frequency Age (years) 0 5 10 15 20 25 30 35 40 45 50 55 60 44 40 36 32 28 24 20 16 12 8 4 0

7. Draw the curve Cumulative frequency Age (years) 0 5 10 15 20 25 30 35 40 45 50 55 60 44 40 36 32 28 24 20 16 12 8 4 0

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

9. Median…… Cumulative frequency Age (years) 0 5 10 15 20 25 30 35 40 45 50 55 60 44 40 36 32 28 24 20 16 12 8 4 0 halfway up Read off here

10. The median is …….. (about) 26.

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

12. Lower Quartile Cumulative frequency Age (years) 0 5 10 15 20 25 30 35 40 45 50 55 60 44 40 36 32 28 24 20 16 12 8 4 0 11 – quarter of 44 Read off here

13. So the lower quartile is …. 19

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

15. Upper quartile Cumulative frequency Age (years) 0 5 10 15 20 25 30 35 40 45 50 55 60 44 40 36 32 28 24 20 16 12 8 4 0 33 – three quarters of 44 Read off here

16. The upper quartile is …. 32

17. Inter-Quartile range Upper quartile – lower quartile

18. 32 - 19

19. Inter-quartile range = 13

20. Try this one ….. Salary (£) Frequency 8001 - 10000 9 10001 - 14000 18 14001 - 18000 23 18001 - 20000 6 20001 - 24000 3 24001 - 30000 1 Salary (£) Cum. Freq. 100009 1400027 1800050 2000056 2400059 3000060

21. Cumulative frequency Constructing a cumulative frequency table Using a cumulative frequency graph to construct a box and whisker diagram

22. A golf club has 200 members. Their ages are shown in the frequency table below. Age (a years)Frequency 0 ≤ a < 108 10 ≤ a < 2026 20 ≤ a < 3032 30 ≤ a < 4045 40 ≤ a < 5037 50 ≤ a < 6029 60 ≤ a < 7016 70 ≤ a < 807 8 +26 +32 +45 +37 +29 +16 +7 Age (a years)Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < 80 8 34 66 111 148 177 193 200 A cumulative frequency (or a “less than”) table can be drawn from this data. How old is the youngest/oldest person?

23. Age (a years) Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < 80 8 34 66 111 148 177 193 200 10 20 30 40 50 60 70 80 8 34 66 111 148 177 193 200 We can now use this to draw a cumulative frequency graph.

24. Age (a years) Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < 80 8 34 66 111 148 177 193 200 We can now use this to draw a cumulative frequency graph.

25. Cumulative Frequency graph. We can now use this to find the following information.. Median Lower quartile Upper quartile Lowest Value Highest Value 37 25 51 0 This information can now be used to draw a box and whisker diagram.. 80 Interquartile range 51 - 25 26