1. Cumulative Frequency
and Box Plots

2. Learning Objectives
• To be able to draw a cumulative
frequency curve and use it to estimate
the median and interquartile range and
draw a box plot

3. Does anybody remember how to draw a
Cumulative Frequency Diagram?

4. Cumulative Frequency Curves
•
Cumulative Frequency = a running total of the data
•
Median = Half way up the Cumulative Frequency
•
Lower Quartile (LQ) = ¼ way up Cum Freq
•
Upper Quartile (UQ) = ¾ way up Cum Freq
•
Inter Quartile Range = UQ - LQ

5. Big Worked Example
The table below shows the number of minutes students were late
for their fun algebra lesson.
(a) Draw a Cumulative Frequency Diagram of the data
(b) Use it to find the Median, Lower Quartile, Upper
Quartile, and Inter Quartile Range
(c) Draw a Box-Plot assuming a minimum time of o minutes
and a maximum of 25 minutes
Time t (mins)
0<t≤5
5 < t ≤ 10
10 < t ≤ 15
Number of
Students
10
16
30
15 < t ≤ 20
22
20 < t ≤ 25
2
Cumulative
Frequency

6. 80
x
x
Cum freq
60
x
Median = Middle Value
40
QUARTILES
•Lower Quartile = ¼ way
•Upper Quartile = ¾ way
x
20
x
5
8½
10
Interquartile Range
12½
15½
15
20
= 15½ - 8½ = 7 mins
25
t mins

7. Does anybody have any idea what a Box
Plot is?

8. Box Plots
•
Box Plots (Box and Whisker Diagram) are another way of displaying
data for comparison
•
To draw a Box Plot we need FIVE pieces of information:
•
–
–
–
–
–
1.
2.
3.
4.
5.
The Minimum Value
Lower Quartile (Q1)
The Median (Q2)
Upper Quartile (Q3)
Maximum Value
They are drawn in the following way:
1
2
3
4
5

9. Box Plot from Cumulative Frequency Curve
70
50
¾
40
¼
10
0
10
20
30
UQ = 38
20
IQR = 38 – 21
= 17 mins
Median = 27
30
½
LQ = 21
Cumulative Frequency
60
40
50
60
70
Minutes Late
0
10
20
30
40
50
60

10. Box Plot
Lowest value
Lower Quartile
0
Highest value
Median
5
10
Upper Quartile
15
20
25
t mins

11. Work
• Ex 7:1
– Page 62
– Questions 5 and 6