Comparing data sets in context | Maths | Quizalize & Oak National Academy

Starter quiz

Which is the modal class?

$0\leq h<20$

$20\leq h<40$ ✓

$40\leq h<60$

$60\leq h<80$
Which class contains the median value?

$0\leq h<20$

$20\leq h<40$ ✓

$40\leq h<60$

$60\leq h<80$
The mean of this list of data: 65, 45, 72, 39, 42, 76, 32, 63, 54, 55 is ______.

'54.3' ✓
Which of these calculations is correct for finding an estimate of the range?

21 − 11

60 − 20

80 − 0 ✓

79 − 1
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.

'1.28' ✓
A gardener records the heights of tomato plants in their greenhouse. An estimate of the mean for this data is ______ cm.

'36' ✓

Exit quiz

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.

Laura could have scored more than Jun on one of the tests. ✓

Laura's typical score was less than Jun's. ✓

Jun scored 83% on at least one of his tests.
The wages of two companies have been analysed. The mean average suggests that company ______ pays its employees more.

'A' ✓
The wages of two companies have been analysed. The median average suggests that company ______ pays its employees more.

'B' ✓
The wages of two companies have been analysed. The modal average suggests that company ______ pays its employees more.

'B' ✓
The wages of two companies have been analysed. The summary statistics suggest that ...

... company A has a wider disparity in the wages of the company than company B. ✓

... 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.
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.

No, home owners may save more or less than £180, the mean is just an average. ✓

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Lesson Details

Key learning points

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

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}.

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.