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Year 8

Statistical problems - statistical summaries

I can choose appropriate statistical measures to explore a statistical problem.

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New
New
Year 8

Statistical problems - statistical summaries

I can choose appropriate statistical measures to explore a statistical problem.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The type of data may mean that certain statistical measures are not appropriate.
  2. The nature of the data may mean that certain statistical measures are not appropriate.
  3. Certain statistical measures may not make sense within the context of the data.

Common misconception

Either the mean, median or mode could be used as an average in any situation.

The choice of average can depend on the type of data. For example, in a list of colours, you can find the mode but not the mean.

Keywords

  • Statistical summary - A statistical summary sums up the features of a data set.

  • Spread - The spread/dispersion of data values describes how far apart the pieces of data are.

  • Central tendency - a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution

Look up the class's data from a recent test or competition. Display the mean median and mode and ask "which average would you prefer me to use for this class?" Tell pupils to imagine the numbers are race times instead. Ask "would your choice change?"
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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Starter quiz

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6 Questions

Q1.
Match each type of average with its description.
Correct Answer:mean,the sum of the data divided by the number of data points

the sum of the data divided by the number of data points

Correct Answer:median,the most central (middle) piece of data

the most central (middle) piece of data

Correct Answer:mode,the data value with the highest frequency

the data value with the highest frequency

Q2.
The spread of a data set can be measured using the , by subtracting the lowest value from the highest value.
Correct Answer: range, RANGE
Q3.
What is the mode for the data represented in the dot plot? The mode is
An image in a quiz
Correct Answer: 3, three
Q4.
What is the median for the data represented in the dot plot? The median is
An image in a quiz
Correct Answer: 4, four
Q5.
Find the mean for following numbers: 1, 4, 7, 8. The mean is
Correct Answer: 5, five
Q6.
Which set of numbers has the greatest range?
Correct answer: 20, 24, 25, 27, 29
23, 24, 25, 29, 29
33, 34, 35, 37, 39
134, 135, 137, 140

Exit quiz

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6 Questions

Q1.
Which statistical summary is not a type of average?
mean
median
mode
Correct answer: range
Q2.
Select the type of average that could be used for the following data: dog, cat, dog, dog, fish, cat, cat, hamster, cat
mean
median
Correct answer: mode
range
Q3.
Each data set has a mean of 50. For which data set is this average the least representative of numbers in the set?
45, 49, 49, 51, 52, 54
49, 49, 50, 50, 50, 52
Correct answer: -337, 109, 120, 131, 138, 139
Q4.
Select the type of average which would least represent the central tendency of the following data: 1, 2, 5, 6, 7, 10, 10
mean
median
Correct answer: mode
Q5.
The table provide a statistical summary of data about monthly rainfall in four regions. Which region tends to get the most rainfall?
An image in a quiz
Armagh
Bradford
Cardiff
Correct answer: Dundee
Q6.
The table provide a statistical summary of data about monthly rainfall in four regions. In which region is the amount of rainfall most consistent?
An image in a quiz
Correct answer: Armagh
Bradford
Cardiff
Dundee