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

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* ***Example:**

**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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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

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 = 16This 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.

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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