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**Cumulative frequency graphs**

How to draw and use….. Cumulative frequency graphs

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**Cumulative frequency is just…**

A running total

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**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 ( )

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**Once we have calculated the cumulative frequency**

We don’t need the frequency any more.

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**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

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**Plot the points 44 40 36 32 28 24 Cumulative 20 frequency 16 12 8 4**

Cumulative frequency Age (years)

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**Draw the curve 44 40 36 32 28 24 Cumulative 20 frequency 16 12 8 4**

Cumulative frequency Age (years)

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

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**Median…… 44 40 36 32 28 24 20 16 12 8 4 Cumulative frequency**

Cumulative frequency halfway up Read off here Age (years)

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The median is …….. (about) 26.

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**Now for the lower quartile**

Quarter of the way up the Cumulative frequency axis

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**Lower Quartile 44 40 36 32 28 11 – quarter of 44 24 Cumulative 20**

16 12 8 4 11 – quarter of 44 Cumulative frequency Read off here Age (years)

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**So the lower quartile is ….**

19

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**Three quarters of the way up the Cumulative frequency axis**

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

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**Upper quartile 33 – three quarters of 44 44 40 36 32 28 24 Cumulative**

20 16 12 8 4 Cumulative frequency Read off here Age (years)

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The upper quartile is …. 32

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**Upper quartile – lower quartile**

Inter-Quartile range Upper quartile – lower quartile

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**Upper quartile – lower quartile**

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**Inter-quartile range =**

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**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

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