cumulative frequency constructing a cumulative frequency table using a cumulative frequency graph to...
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Cumulative frequency
•Constructing a cumulative frequency table
•Using a cumulative frequency graph to construct a box and whisker diagram
A golf club has 200 members. Their ages are shown in the frequency table below.
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
8
+26
+32
+45
+37
+29
+16
+7
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
A cumulative frequency (or a “less than”) table can be drawn from this data.
How old is the youngest/oldest person?
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age of member
Cu
mu
lati
ve f
req
uen
cy
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
10
20
30
40
50
60
70
80
8
34
66
111
148
177
193
200
We can now use this to draw a cumulative frequency graph.
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age of member
Cu
mu
lati
ve f
req
uen
cy
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
We can now use this to draw a cumulative frequency graph.
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age of member
Cu
mu
lati
ve f
req
uen
cy
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age of member
Cu
mu
lative freq
uen
cy
Cumulative Frequency graph.
We can now use this to find the following information..
Median
Lower quartile
Upper quartile
Lowest Value
Highest Value
37
25
51
0
This information can now be used to draw a box and whisker diagram..
80
Interquartile range 51 - 2526