How to draw and use Cumulative frequency graphs

How to draw and use…. . Cumulative frequency graphs

Cumulative frequency is just… A running total

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

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

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

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

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

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

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

The median is ……. . (about) 26.

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

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

So the lower quartile is …. 19

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

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

The upper quartile is …. 32

Inter-Quartile range Upper quartile – lower quartile

Upper quartile – lower quartile 32 - 19

Inter-quartile range = 13

Try this one …. . Salary (£) Frequency Salary (£) Cum. Freq. 8001 - 10000 9 10001 - 14000 18 14000 27 14001 - 18000 23 18000 50 18001 - 20000 6 20000 56 20001 - 24000 3 24000 59 24001 - 30000 1 30000 60