Year 11 - Maths
Interpreting a cumulative frequency graph
Graphical representations of data: cumulative frequency and histograms
Study Hub
Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils consider cumulative frequency graphs and histograms, and compare these with other known graphical representations.
Lesson Summary
You will learn to interpret a cumulative frequency graph.
Key Notes
- A cumulative frequency has values read in the same way as a line graph
- The median is the 50th percentile
- The lower quartile is the 25th percentile
- The upper quartile is the 75th percentile
- Other percentiles can also be found
Vocabulary To Learn
- Percentile: A percentile is a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it.
- Lower quartile: The lower quartile is the value under which 25% of data points are found when they are arranged in increasing order. Also known as the first quartile (Q1).
- Upper quartile: The upper quartile is the value under which 75% of data points are found when they are arranged in increasing order. Also known as the third quartile (Q3).
Common Mistakes To Avoid
- Using the highest value on the y-axis rather than the total frequency when calculating the values to read off for the lower quartile, median and upper quartile.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A cumulative frequency has values read in the same way as a line graph. The median is the 50th percentile.
2. Use this key word in a maths sentence and explain it clearly. 'Percentile'
A percentile is a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Using the highest value on the y-axis rather than the total frequency when calculating the values to read off for the lower quartile, median and upper quartile. Correction: Ensure pupils understand that the total frequency must be used. A graph where the y-axis goes up to 100 and the total frequency is 40 can be used to highlight this. Then repeat with the same data, but with a graph where the y-axis goes up to 200.
More Lessons In This Unit
- Comparing box plots Study Guide
- Constructing a cumulative frequency graph Study Guide
- Constructing box plots Study Guide
- Constructing histograms and box plots using technology Study Guide
- Histograms with equal bar width Study Guide
- Histograms with unequal bar width Study Guide
- Interquartile range Study Guide
- Moving between tables and histograms Study Guide
- Problem solving with cumulative frequency and histograms Study Guide
- Summary statistics from histograms Study Guide
Browse all guides in the Year 11 Maths guide library.