OML Search

Median, Quartiles And Percentiles (Grouped Data)

Related Topics:
More Statistics Lessons

In this lesson, we will learn how to obtain the median, quartiles and percentiles from the cumulative frequency graph of the distribution (grouped data).



Example:

The following cumulative frequency graph shows the distribution of marks scored by a class of 40 students in a test.

Percentiles on Cumulative Frequency Graph

Use the graph to estimate

a) the median mark b) the upper quartile

c) the lower quartile d) the interquartile range

Solution:

a) Median corresponds to the 50th percentile i.e. 50% of the total frequency.

50% of the total frequency =

From the graph, 20 on the vertical axis corresponds to 44 on the horizontal axis. The median mark is 44.

b) The upper quartile corresponds to the 75th percentile i.e. 75% of the total frequency.

75% of the total frequency =

From the graph, 30 on the vertical axis corresponds to 52 on the horizontal axis. The upper quartile is 52.

c) The lower quartile corresponds to the 25th percentile i.e. 25% of the total frequency.

25% of the total frequency =

From the graph, 10 on the vertical axis corresponds to 36 on the horizontal axis. The lower quartile is 36.

d) The interquartile range = upper quartile – lower quartile
= 52 – 36 = 16




How cumulative frequency diagrams are used to estimate the median and quartiles of a frequency distribution? Cumulative Frequency - Finding the Median and Interquartile Range for Grouped Data Reading Cumulative Frequency Graphs
This video shows you how to interpret cumulative frequency graphs. It shows you how to find the median, lower quartile, upper quartile and interquartile range, IQR. Cumulative Frequency Curve
This video helps you to understand how to work out cumulative frequency, draw the cumulative frequency graph and find the median, lower quartile, upper quartile and interquartile range.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget


OML Search


We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.