Year 11 - Maths
Moving between tables 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 construct a table from a histogram.
Key Notes
- A frequency table can be used to construct a histogram
- A histogram can be used to construct a frequency table
- Data is sometimes collected using uneven class widths
Vocabulary To Learn
- Continuous data: Continuous data can take any value within a range. (Height, mass, temperature)
- 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.
- Frequency density: Frequency density is proportional to the frequency per unit for the data in each class. Often, the multiplier is 1 meaning that frequency density = frequency ÷ class width.
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.
A frequency table can be used to construct a histogram. A histogram can be used to construct a frequency table.
2. Use this key word in a maths sentence and explain it clearly. 'Continuous data'
Continuous data can take any value within a range. (Height, mass, temperature). 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
- Problem solving with cumulative frequency and histograms Study Guide
- Summary statistics from histograms Study Guide
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