Year 11 - Maths
Summary statistics from 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 estimate the mean and median from a histogram.
Key Notes
- The mean can be found using a histogram
- The median can be found using a histogram
- An estimate for the frequency within a given data range can be found
Vocabulary To Learn
- Arithmetic mean: The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.
- 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.
- 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.
The mean can be found using a histogram. The median can be found using a histogram.
2. Use this key word in a maths sentence and explain it clearly. 'Arithmetic mean'
The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values. 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
- Problem solving with cumulative frequency and histograms Study Guide
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