In these lessons, we will learn how to draw a cumulative frequency graph (cumulative frequency curve) and how to find the median, quartiles and inter-quartile range.
Related Topics: More Statistics Lessons
A Cumulative Frequency Graph is a graph plotted from a cumulative frequency table. A cumulative frequency graph is also called an ogive or cumulative frequency curve.
Example :
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.
The following video shows how to obtain a cumulative frequency graph from a cumulative frequency table.
Calculate the cumulative frequency. Write down the upper class boundaries. Plot the cumulative frequency curve. Find the median values. Find the upper and lower quartiles. Find the inter-quartile range.
How to draw a cumulative frequency curve from a cumulative frequency table and how to calculate the median and interquartile range.