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**Cumulative Frequency Diagrams & Box Plots**

OCR Stage 8

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**Cumulative Frequency Time t minutes 0≤t<5 5≤t<10 10≤t<15**

Number of students 10 16 30 22 2 Cumulative Frequency 10 26 56 78 80

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**80 x x Cum freq Interquartile Range = 15½ - 8½ = 7 mins 60 x**

Median = Middle Value 40 QUARTILES Lower Quartile = ¼ way Upper Quartile = ¾ way x 20 x 8½ 12½ 15½ 5 10 15 20 25 t mins t minutes 0≤t<5 5≤t<10 10≤t<15 15≤t<20 20≤t<25 CF 10 26 56 78 80

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**Box Plot Lowest value Median Highest value Lower Quartile**

Upper Quartile 5 10 15 20 25 t mins

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**Comparing 2 sets of data Cum freq Median = 62kg Upper Quartile = 70kg**

Lower Quartile = 52kg Interquartile range = 70 – 52 = 18kg

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**Comparing 2 sets of data Cum freq Median = 78kg Upper Quartile = 89kg**

Lower Quartile = 66kg Interquartile range = 89 – 66 = 23kg

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**Box Plots IQRs MEDIANS Median = 78kg Lower Quartile = 66kg**

Highest = 112 Lowest = 40 Upper Quartile = 89kg Median = 62kg Lower Quartile = 52kg Highest = 96 Lowest = 34 Upper Quartile = 70kg GIRLS BOYS 40 60 80 100 120 m kg 20 18 IQRs MEDIANS 23 78 and 62

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**Comparison statements**

Boys have a larger MEDIAN so on average, they are heavier than girls the average boy is 16kg heavier than the average girl Boys have larger Interquartile Range so boys’ weights vary more than girls’ weights Why do we NOT use the Range? One extreme value can distort the comparison

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