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.

Comparing data sets in context

Maths

In this unit, pupils began to compare two different sets of data. In the future unit, pupils will consider cumulative frequency graphs and histograms and compare the data from these diagrams to other graphical representations.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils extend this learning to comparing two different data sets and comparing these measures of central tendency.

Comparisons of numerical summaries of data

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.

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?

The wages of two companies have been analysed. The mean average suggests that company {{ }} pays its employees more. 

The wages of two companies have been analysed. The median average suggests that company {{ }} pays its employees more.

The wages of two companies have been analysed. The modal average suggests that company {{ }} pays its employees more.

... 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.

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

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, home owners may save more or less than £180, the mean is just an average.

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?

The mean of this list of data: 65, 45, 72, 39, 42, 76, 32, 63, 54, 55 is {{ }}.

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

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.

A gardener records the heights of tomato plants in their greenhouse. An estimate of the mean for this data is {{ }} cm.

Starter Quiz