Cumulative Frequency Diagrams & Box Plots

OCR Stage 8

Cumulative Frequency

Time

t minutes0≤t<5 5≤t<10 10≤t<15 15≤t<20 20≤t<25

Number of students

10 16 30 22 2

Cumulative Frequency

10 26 56 78 80

5 10 15 20 25 t mins

Cum freq

20

40

60

80

x

x

x

x x

Median = Middle Value

QUARTILES•Lower Quartile = ¼ way•Upper Quartile = ¾ way

Interquartile Range

8½ 15½12½

= 15½ - 8½ = 7 mins

t minutes 0≤t<5 5≤t<10 10≤t<15 15≤t<20 20≤t<25

CF 10 26 56 78 80

Box Plot

5 10 15 20 25 t mins0

Lowest value Highest valueMedian

Lower Quartile Upper Quartile

Cum

fre

qComparing 2 sets of data

Median = 62kg

Lower Quartile = 52kg

Upper Quartile = 70kg

Interquartile range = 70 – 52 = 18kg

Cum

fre

qComparing 2 sets of data

Median = 78kg

Lower Quartile = 66kg

Upper Quartile = 89kg

Interquartile range = 89 – 66 = 23kg

Box Plots

40 60 80 100 120 m kg20

IQRs18

23MEDIANS 78 and 62

BOYS

GIRLS

Median = 78kg

Lower Quartile = 66kg

Highest = 112Lowest = 40

Upper Quartile = 89kg

Median = 62kg

Lower Quartile = 52kg

Highest = 96Lowest = 34

Upper Quartile = 70kg

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