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 0 < t ≤ 5 5 < t ≤ 10 10 < t ≤ 15
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)
Number of Students
Cumulative Frequency
0 < t ≤ 5 10
5 < t ≤ 10 16
10 < t ≤ 15 30
15 < t ≤ 20 22
20 < t ≤ 25 2

6. 80 x x
Cum freq 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
Interquartile Range
= 15½ - 8½ = 7 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. The Minimum Value
2. Lower Quartile (Q1)
3. The Median (Q2)
4. Upper Quartile (Q3)
5. Maximum Value
They are drawn in the following way:
BOX = The location of the middle 50% of the data
WHISKERS = How the data is spread overall 3 4 1 2 5

9. Box Plot from Cumulative Frequency Curve10 20 30 40 50 60 70
Cumulative Frequency
Minutes Late
Median = 27
LQ = 21
UQ = 38
IQR = 38 – = 17 mins 10 20 30 40 50 60

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

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