The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.

The median is the central (middle) piece of data when the data are in numerical order. It is a measure of central tendency representing the average of the values.

The mode is the most frequent value. It is a measure of central tendency representing the average of the values.

The range is a measure of spread. It is found by finding the difference between the highest and lowest values.

The population is the entire set of people, creatures, plants or items that make up the whole group which is being studied.

Checking understanding of statistical problems

Maths

In this unit, pupils are given the opportunity to assess how valid a sample may be and what the averages might tell us. In the future unit, pupils extend their knowledge of averages to stem and leaf diagrams as well as comparing two data sets.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils are given the opportunity to consider where the data came from and how it was collected and can therefore start to evaluate how good a representation the sample is of the whole population.

Sampling

Data has been collected and processed about the number of sweets per packet in 3 different multipacks. The company claims ‘an average of 12 sweets per pack’. Which multipack best supports the claim? 

Izzy’s variety of scores is greater than Jun’s.

Izzy’s middle score was lower than Jun’s.

Izzy’s average, typical score is higher than Jun’s.

Izzy’s most common score is the higher than Jun’s. 

The total of Izzy's maths scores is higher than Jun's

Izzy and Jun compare their scores in their last 10 maths tests. The tables show the summary statistics. Select the statements that are correct about their **mean** scores.

Izzy and Jun compare their scores in their last 10 maths tests. The tables show the summary statistics. Select the statement that is correct about their **median** scores.

Yes, the sample is representative of all adults.

No, Jacob's sample is biased as people in the library are more likely to read.

No, Jacob needs to survey more people from the library to be sure.

No, Jacob needs to survey people from the library on different days to be sure.

Jacob went to the library and surveyed 10 adults in the library to find out how many books they read in a month. The mean was 2 books. Jacob says, "All adults read 2 books a month." Is he correct?

There is more variability in the number of frosty days in York.

York is likely to be colder in December than Bristol as the average is higher.

Bristol has more frosty days than York as the range is higher.

There is more variability in the number of frosty days in Bristol.

Bristol is likely to be colder in December than York as the range is higher.

The table of summary statistics shows the number of days of air frost each day in December over the last 10 years. Select the correct statements.

The middle (central) piece of data when the data are in order

Sum of the data values divided by the number of values

Match each summary statistic to its definition.

Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The modal number of sweets is {{ }}.

Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The median number of sweets is {{ }}.

Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The mean number of sweets is {{ }}.

Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The range in the number of sweets is {{ }}.

This set of data has two values missing. $$\square$$, 5, 6, 7, 8, $$\square$$, 5, 6, 8. The mean of the data is 6, the mode is 5 and the median is 6. Select the missing data values.

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