1. Cumulative Frequency Diagrams & Box Plots
OCR Stage 8

2. 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

3. 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

4. Box Plot Lowest value Median Highest value Lower Quartile
Upper Quartile 5 10 15 20 25
t mins

5. Comparing 2 sets of data Cum freq Median = 62kg Upper Quartile = 70kg
Lower Quartile = 52kg
Interquartile range
= 70 – 52 = 18kg

6. Comparing 2 sets of data Cum freq Median = 78kg Upper Quartile = 89kg
Lower Quartile = 66kg
Interquartile range
= 89 – 66 = 23kg

7. 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

8. 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