Draw a cumulative frequency graph for the frequency table below.
Length (x mm) |
Frequency |
11 – 15 |
2 |
16 – 20 |
4 |
21 – 25 |
8 |
25 – 30 |
14 |
31 – 35 |
6 |
36 – 40 |
4 |
41 – 45 |
2 |
Solution:
We need to add a class with 0 frequency before the first class and then find the upper boundary for each class interval.
Length (x mm) |
Frequency |
Upper Class Boundary |
Length (x mm) |
Cumulative Frequency |
6 – 10 |
0 |
10.5 |
x ≤ 10.5 |
0 |
11 – 15 |
2 |
15.5 |
x ≤ 15.5 |
2 |
16 – 20 |
4 |
20.5 |
x ≤ 20.5 |
6 |
21 – 25 |
8 |
25.5 |
x ≤ 25.5 |
14 |
25 – 30 |
14 |
30.5 |
x ≤ 30.5 |
28 |
31 – 35 |
6 |
35.5 |
x ≤ 35.5 |
34 |
36 – 40 |
4 |
40.5 |
x ≤ 40.5 |
38 |
41 – 45 |
2 |
45.5 |
x ≤ 45.5 |
40 |
And then plot the cumulative frequency against the upper class boundary of each interval and join the points with a smooth curve.
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