Year 11 - Maths
Problem solving with cumulative frequency and histograms
Graphical representations of data: cumulative frequency and histograms
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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 use your knowledge of cumulative frequency and histograms to solve problems.
Key Notes
- Different representations of the same data set give a fuller picture
- It is important to identify what features are used to analyse a data set
- It is important to identify what features are used to compare two data sets
Vocabulary To Learn
- Box plot: A box plot is a diagram that clearly shows the minimum and maximum value of a data set long with the three quartiles.
- 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).
- Histogram: A histogram is a diagram consisting of rectangles whose area is proportional to the frequency in each class and whose width is equal to the class interval.
Common Mistakes To Avoid
- Histograms with unequal bar widths are plotted against the frequency and/or pupils read the frequency density as the frequency of the class width.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Different representations of the same data set give a fuller picture. It is important to identify what features are used to analyse a data set.
2. Use this key word in a maths sentence and explain it clearly. 'Box plot'
A box plot is a diagram that clearly shows the minimum and maximum value of a data set long with the three quartiles. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Histograms with unequal bar widths are plotted against the frequency and/or pupils read the frequency density as the frequency of the class width. Correction: Show what a histogram with unequal bar widths looks like when plotted against frequency. This visual aid will show pupils the distribution of data is difficult to see.
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
- Interpreting a cumulative frequency graph Study Guide
- Interquartile range Study Guide
- Moving between tables and histograms Study Guide
- Summary statistics from histograms Study Guide
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