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Year 8

Summarising data

I can see that the different measures of central tendency offer a summary of a set of data.

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New

Year 8

Summarising data

I can see that the different measures of central tendency offer a summary of a set of data.

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Share activities with pupils

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Lesson details

Key learning points

The mode is a useful measure of central tendency for certain data sets.
The median is a useful measure of central tendency for certain data sets.
The mean is a useful measure of central tendency for certain data sets.

Keywords

Data - Data are a collection of information.
Mean - The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of 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.
Measure of central tendency - A summary that attempts to describe a whole set of data with a single value that represents the middle of the distribution.

Common misconception

The mean is the most meaningful average.

Looking at bimodal data, trimodal data or data with extreme outliers. Context may be relevant.

Consider using interactive and spreadsheet software to extend ideas into larger data sets and to model different situations. Looking at how the different averages fall compared to a dot plot or bar chart.

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 the summary statistic to its definition.

Correct Answer:mean,is the sum of the values divided by the number of values

is the sum of the values divided by the number of values

Correct Answer:median,is the middle piece of data when the data are in order

is the middle piece of data when the data are in order

Correct Answer:mode,is the most frequent value

is the most frequent value

Correct Answer:range,is a measure of spread

is a measure of spread

Q2.

Find the mode of this list of numbers: 4, 7, 16, 16, 22, 23, 24, 28

Correct answer: 16

17.5

Q3.

Find the median of this list of numbers. 4, 7, 16, 16, 22, 23, 24, 28

17.5

Correct answer: 19

Q4.

Find the modal value of this dataset from its dot plot.

Correct answer: 29

Q5.

Work out the mean of this dataset: (-6), (-5), (-3), (-3), 1, 4, 5, 7

Correct Answer: 0, zero

Q6.

Dataset A and dataset B both show the minimum temperatures in two different locations. How much bigger is the range of dataset A than the range of dataset B?

Correct Answer: 11, eleven

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Exit quiz

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6 Questions

Q1.

Which of these most closely describe a "measure of central tendency"?

A single value that summarises how spread out or varied a dataset is

Always a single value that calculates the middle number in an ordered dataset

Usually a single value that calculates the middle number in an ordered dataset

Always a single value representing a central property of a distribution

Correct answer: Usually a single value representing a central property of a distribution

Q2.

Describe the modal properties of this dataset: 2, 2, 6, 5, 6, 6, 3, 4, 0, 9, 2

mode at 2

mode at 6

bimodal at 2 and 5

Correct answer: bimodal at 2 and 6

trimodal at 2, 5, and 6

Q3.

For the following dataset, match the summary statistic to its value: 10, 14, 14, 18, 19, 21, 23

Correct Answer:mean,17

Correct Answer:median,18

Correct Answer:mode,14

Correct Answer:range,13

Q4.

Which of these is the most likely value of the mean for this dataset, represented by a dot plot?

Correct answer: 80

Q5.

In which of these dot plots would the mode be a representative summary of the dataset?

Correct answer: b

Correct answer: d

Q6.

Which of the following statements are true for this dot plot when evaluating whether the median is a representative summary of the data?

Correct answer: The median is approximately 21.

The median is approximately 17 and 26.

Correct answer: The median may not be the most representative summary.

The median will never be a useful summary for this dataset.

Correct answer: The median can still be a useful summary for this dataset.

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