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Year 10
Higher

Checking understanding of measures of central tendency

I can identify the limitations of each measure of central tendency and identify which should be used.

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New
New
Year 10
Higher

Checking understanding of measures of central tendency

I can identify the limitations of each measure of central tendency and identify which should be used.

Download all resources
Share activities with pupils

Lesson details

Key learning points

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

Common misconception

Mean, median and mode are only useful if they are close together.

If the mean is significantly higher or lower than the other averages, this suggests an extreme value in the data set.

Keywords

  • Measure of central tendency - A measure of central tendency is 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.

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

Challenge pupils to create their own data sets where mean > median > mode and data sets where mode > mean > median. What do they notice about the features of these data sets?
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.
Which of these is not a measure of central tendency?
mean
median
mode
Correct answer: range
Q2.
The mode of this data set is 6. Which of these values can $$x$$ take?
An image in a quiz
5
Correct answer: 6
7
Correct answer: 13
Q3.
The mean of this data set is 5, so $$x$$ is .
An image in a quiz
Correct Answer: 1, one
Q4.
The range of this data set is 5. What could the values of $$x$$ be?
An image in a quiz
1
Correct answer: 2
Correct answer: 10
11
12
Q5.
The median of this set of data is 6. Which of these describe all the values $$x$$ be?
An image in a quiz
$$x$$ has to be more than 6
$$x$$ has to be more than 7
$$x$$ has to be less than 5
$$x$$ has to be 6
Correct answer: $$x$$ can be any number
Q6.
Match each letter to the number it represents.
An image in a quiz
Correct Answer:$$a$$,6

6

Correct Answer:$$b$$,700

700

Correct Answer:$$c$$,70

70

Correct Answer:$$d$$,50

50

Correct Answer:$$e$$,2100

2100

Correct Answer:$$f$$,42

42

Exit quiz

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6 Questions

Q1.
In which of these data sets is the mean more likely to be influenced by outliers or unsymmetrical data?
23, 26, 27, 27, 29, 31
Correct answer: 24, 27, 29, 29, 32, 59
Correct answer: 13, 37, 37, 39, 40, 41
42, 44, 45, 46, 48
Q2.
Which of these measures of central tendency can be used to summarise qualitative data?
mean
median
Correct answer: mode
Q3.
This dot plot shows a data set where the mode = median = 48. Will the mean be less than 48, equal to 48 or more than 48?
An image in a quiz
less than 48
equal to 48
Correct answer: more than 48
Q4.
Select the true statements for the data set: 8, 13, 8, 11, 10, 13, 8, 11, 12, 10.
The most frequent data point is 3.
Correct answer: The most frequent data point is 8.
The modal value occurs 2 times.
Correct answer: The modal value occurs 3 times.
The modal value occurs 8 times.
Q5.
Which of the measures of central tendency would be the most appropriate measure for the shopkeeper to use to know how many carrier bags to order?
An image in a quiz
mean
Correct answer: median
mode
Q6.
The average house price on a street of 8 houses is advertised at £400 000. A local estate agent values 7 houses below £400 000. Which average has been used in the quoted £400 000?
Correct answer: mean
median
mode