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Year 10
Higher

Comparing data sets in context

I can use measures of central tendency and spread to compare two data sets in context.

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New
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Year 10
Higher

Comparing data sets in context

I can use measures of central tendency and spread to compare two data sets in context.

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Share activities with pupils
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Lesson details

Key learning points

  1. Data can be hard to compare when presented in lists and tables.
  2. Statistical summaries can be calculated to compare data sets.
  3. Statistical summaries do not always provide enough information by themselves.

Keywords

  • A statistical summary - sums up the features of a data set. It may contain the average (mean, median and/or mode) which measures the central tendency. It may also contain the range which measures the spread.

Common misconception

Pupils may feel that one statistical summary is enough to compare two data sets.

Highlight to pupils that the more information you know, the better your understanding of a data set and therefore a more comprehensive comparison can take place. Compare the means of {-120, -100, -50, 0, 1000} and {145, 145, 146, 147, 147}.

Ask the pupils to come up with small data sets where the either the mean, mode, median or range is fixed and compare/discuss the variety of answers. You can increase the amount of statistical summaries to see that the more you have the harder it is to make your data sets unique.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which is the modal class?
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$$0\leq h<20$$
Correct answer: $$20\leq h<40$$
$$40\leq h<60$$
$$60\leq h<80$$
Q2.
Which class contains the median value?
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$$0\leq h<20$$
Correct answer: $$20\leq h<40$$
$$40\leq h<60$$
$$60\leq h<80$$
Q3.
The mean of this list of data: 65, 45, 72, 39, 42, 76, 32, 63, 54, 55 is .
Correct Answer: 54.3
Q4.
Which of these calculations is correct for finding an estimate of the range?
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21 − 11
60 − 20
Correct answer: 80 − 0
79 − 1
Q5.
A football coach records the number of goals scored in their team's last 50 matches and records the results in a table. The mean number of goals per match is goals.
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Correct Answer: 1.28
Q6.
A gardener records the heights of tomato plants in their greenhouse. An estimate of the mean for this data is cm.
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Correct Answer: 36, thirty six, 36 cm

Exit quiz

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6 Questions

Q1.
Laura and Jun compare their mean scores on their recent tests. Laura has a mean of 75% and Jun has a mean of 83%. Which statements are true?
Jun scored better than Laura on all of the tests.
Jun's typical score was lower than Laura's.
Correct answer: Laura could have scored more than Jun on one of the tests.
Correct answer: Laura's typical score was less than Jun's.
Jun scored 83% on at least one of his tests.
Q2.
The wages of two companies have been analysed. The mean average suggests that company pays its employees more.
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Correct Answer: A, a
Q3.
The wages of two companies have been analysed. The median average suggests that company pays its employees more.
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Correct Answer: B, b
Q4.
The wages of two companies have been analysed. The modal average suggests that company pays its employees more.
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Correct Answer: B, b
Q5.
The wages of two companies have been analysed. The summary statistics suggest that ...
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Correct answer: ... company A has a wider disparity in the wages of the company than company B.
Correct answer: ... company B's wages are more similar to each other than company A's wages.
... company A pays most of its employee's above the mean wage.
... company B pays most of its employee's above the median wage.
... company B has 4 employees.
Q6.
An advert for insulation claims that all homeowners with their insulation save £180 per year on heating bills. This claim is based on the mean average price reduction. Is this a fair claim?
Yes, the mean has taken into account all savings so doesn't ignore any data.
Yes, the mean represents the amount each home owner saves
No, they should use the median or mode.
Correct answer: No, home owners may save more or less than £180, the mean is just an average.