1. Constructing a cumulative frequency table
Using a cumulative frequency graph to construct a box and whisker diagram

2. 0 ≤ a < 10 8 10 ≤ a < 20 26 20 ≤ a < 30 32 30 ≤ a < 40 45
A golf club has 200 members. Their ages are shown in the frequency table below.
A cumulative frequency (or a “less than”) table can be drawn from this data.
Age (a years)
Frequency
0 ≤ a < 10 8
10 ≤ a < 20 26
20 ≤ a < 30 32
30 ≤ a < 40 45
40 ≤ a < 50 37
50 ≤ a < 60 29
60 ≤ a < 70 16
70 ≤ a < 80 7
Age (a years)
Cumulative frequency
a < 10
a < 20
a < 30
a < 40
a < 50
a < 60
a < 70
a < 80 8 8
+26 34
+32 66
+45
111
+37
148
+29
177
+16
193 +7
200
How old is the youngest/oldest person?

3. a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70
We can now use this to draw a cumulative frequency graph.
Age (a years)
Cumulative frequency
a < 10
a < 20
a < 30
a < 40
a < 50
a < 60
a < 70
a < 80 10 8 8 20 34 34 30 66 66 40
111
111 50
148
148 60
177
177 70
193
193 80
200
200

4. a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70
We can now use this to draw a cumulative frequency graph.
Age (a years)
Cumulative frequency
a < 10
a < 20
a < 30
a < 40
a < 50
a < 60
a < 70
a < 80 8 34 66
111
148
177
193
200

5. Cumulative Frequency graph.
We can now use this to find the following information..
Median 37
Lower quartile 25
Upper quartile 51
Lowest Value
Highest Value 80
Interquartile range 26
This information can now be used to draw a box and whisker diagram..