# Cumulative Frequency Graph

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

What is a Cumulative Frequency Graph?
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. The following examples show how to draw a cumulative frequency curve for grouped data.

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.

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?
How to draw a cumulative frequency curve from a cumulative frequency table and how to estimate the median, quartiles and interquartile range. What are Cumulative Frequency Diagrams?
Investigating cumulative frequencies and cumulative frequencies diagrams. Cumulative Frequency - Median and Quartiles
Investigating how cumulative frequency diagrams are used to estimate the median and quartiles of a frequency distribution.

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