Year 10 - Maths
Calculating summary statistics from stem and leaf diagrams
Comparisons of numerical summaries of data
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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 will compare two different data sets and compare different measures of central tendancy when interpreting the data. Pupils will learn to interrogate frequency tables and stem and leaf diagrams both with and without technology.
Lesson Summary
You will learn to calculate the mean, median, mode and range from a stem and leaf diagram.
Key Notes
- The range can be calculated from a stem and leaf diagram.
- The mode can be calculated from a stem and leaf diagram.
- The median can be calculated from a stem and leaf diagram.
- Although possible, the mean is very time consuming to calculate.
Vocabulary To Learn
- Stem and leaf diagram: A stem and leaf diagram is a systematic way to organise and represent numerical data, by splitting each value into a stem and a leaf.
- 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.
- Median: The median is the central (middle) piece of data when the data are in numerical order.
- Mode: Mode is the most frequent value. It is a measure of central tendency representing the average of the values.
- Range: The range is a measure of spread. It is found by finding the difference between the two extreme points; the lowest and highest values.
Common Mistakes To Avoid
- You can only find the median class from a stem-and-leaf diagram.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The range can be calculated from a stem and leaf diagram. The mode can be calculated from a stem and leaf diagram.
2. Use this key word in a maths sentence and explain it clearly. 'Stem and leaf diagram'
A stem and leaf diagram is a systematic way to organise and represent numerical data, by splitting each value into a stem and a leaf. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: You can only find the median class from a stem-and-leaf diagram. Correction: The data is organised into intervals based on place value. However the full data is still available so the middle value(s) can still be found. The diagram is a form of an ordered list so previous methods for finding the median still apply.
More Lessons In This Unit
- Calculating summary statistics from a grouped frequency table Study Guide
- Calculating the mean from a grouped frequency table Study Guide
- Checking understanding composite and bar-line charts Study Guide
- Checking understanding of bar charts and pictograms Study Guide
- Checking understanding of measures of central tendency Study Guide
- Checking understanding of pie charts Study Guide
- Checking understanding of summary statistics from a frequency table Study Guide
- Checking understanding of summary statistics from a list Study Guide
- Comparing data sets in context Study Guide
- Comparing various representations of data sets Study Guide
- Constructing stem and leaf diagrams Study Guide
- Problem solving with comparisons of numerical data Study Guide
- Statistical summaries using technology Study Guide
- Weighted means Study Guide
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