New
New
Year 10
Foundation

Calculating summary statistics from stem and leaf diagrams

I can calculate the mean, median, mode and range from a stem and leaf diagram.

New
New
Year 10
Foundation

Calculating summary statistics from stem and leaf diagrams

I can calculate the mean, median, mode and range from a stem and leaf diagram.

Lesson details

Key learning points

  1. The range can be calculated from a stem and leaf diagram.
  2. The mode can be calculated from a stem and leaf diagram.
  3. The median can be calculated from a stem and leaf diagram.
  4. Although possible, the mean is very time consuming to calculate.

Common misconception

You can only find the median class from a stem-and-leaf diagram.

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.

Keywords

  • 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.

Challenge pupils to start looking at the shape made by the stem-and-leaf diagrams. Ask them to describe some. Using a big data set and representing it in this way is a great way to zoom out to see the shape of the data and in on the detail. Link with summary statistics, bard charts etc.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
A statistical summary sums up the features of a data set. It may contain an which measures the central tendency. It may also contain the range which measures the spread.
Correct Answer: average
Q2.
The mode of this data set is .
An image in a quiz
Correct Answer: 23, twenty three, twenty-three
Q3.
The range of this data set is .
An image in a quiz
Correct Answer: 7, seven
Q4.
The median of this data set is .
An image in a quiz
Correct Answer: 25, twenty five
Q5.
The mean of this this data set is .
An image in a quiz
Correct Answer: 26, twenty six
Q6.
This table represents the number of cars in 40 households. The mean number of cars per household is cars.
An image in a quiz
Correct Answer: 1.25

6 Questions

Q1.
The modal group in this stem and leaf diagram is __________.
An image in a quiz
30 km - 39 km
Correct answer: 40 km - 49 km
50 km - 59 km
60 km - 69 km
Q2.
The modal distance is km.
An image in a quiz
Correct Answer: 42
Q3.
The range of the data shown on this stem and leaf diagram is km.
An image in a quiz
Correct Answer: 34, thirty four, thirty-four
Q4.
The total of the first row of leaves is kg.
An image in a quiz
Correct Answer: 256, 256 kg
Q5.
Sam and Andeep draw a back-to-back stem and leaf diagram to compare their classes' scores in a quiz. Match the summary statistic for each class with its value.
An image in a quiz
Correct Answer:Sam's class: range,39

39

Correct Answer:Sam's class: mode,31

31

Correct Answer:Sam's class: median,54

54

Correct Answer:Andeep's class: range,34

34

Correct Answer:Andeep's class: mode,42

42

Correct Answer:Andeep's class: median,42.5

42.5

Q6.
Calculate the mean mass (to 2 decimal places) of the data represented in this stem and leaf diagram. The totals for each row have been calculated already.
An image in a quiz
Correct Answer: 80.64 kg, 80.64, 80.64kg