Cumulative Frequency Diagrams & Box Plots OCR Stage 8
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