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Published byAndrea Houston Modified over 7 years ago

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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) 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)

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

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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

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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

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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…… 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

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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 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

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So the lower quartile is …. 19

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

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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

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The upper quartile is …. 32

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Inter-Quartile range Upper quartile – lower quartile

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32 - 19

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Inter-quartile range = 13

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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

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

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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?

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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.

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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.

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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

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