The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values.

The median is the central (middle) piece of data when the data are in numerical order.

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

A summary that attempts to describe a whole set of data with a single value that represents the middle of the distribution.

Summarising data

Maths

Checking understanding of the mean

Calculating the mean

Understanding the median

Calculating the median

Understanding the mode

Calculating the mode

Understanding and calculating the range

Changing a data point

Evaluating the range

Comparing statistical representations

Comparing summaries of data

Analysing different statistical representations

Correlation

Statistical problems - data collection

Statistical problems - statistical summaries

Statistical problems - data presentations

Statistical problems - drawing conclusions

Problem solving with numerical summaries of data

In this unit, pupils consider the mean, median and mode and evaluate their usefulness in a variety of contexts. In the sampling 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.

In this unit, pupils learnt how to calculate the mean and began to use the mean to make comparisons between two sets of data. Pupils also considered whether the mean was an appropriate way of representing the data 

In this unit pupils explore the concept of measures of central tendancy, developing understanding of different types of average and their relative benefits and drawbacks. We then investigate other summaries of data such as the range and data comparison techniques.

Numerical summaries of data

A single value that summarises how spread out or varied a dataset is

Always a single value that calculates the middle number in an ordered dataset

Usually a single value that calculates the middle number in an ordered dataset

Always a single value representing a central property of a distribution

Usually a single value representing a central property of a distribution

Which of these most closely describe a "measure of central tendency"?

Describe the modal properties of this dataset: 2, 2, 6, 5, 6, 6, 3, 4, 0, 9, 2

For the following dataset, match the summary statistic to its value: 10, 14, 14, 18, 19, 21, 23

Which of these is the most likely value of the mean for this dataset, represented by a dot plot?

In which of these dot plots would the mode be a representative summary of the dataset?

The median may not be the most representative summary.

The median will never be a useful summary for this dataset.

The median can still be a useful summary for this dataset.

Which of the following statements are true for this dot plot when evaluating whether the median is a representative summary of the data?

is the sum of the values divided by the number of values

is the middle piece of data when the data are in order

Match the summary statistic to its definition.

Find the mode of this list of numbers: 4, 7, 16, 16, 22, 23, 24, 28

Find the median of this list of numbers. 4, 7, 16, 16, 22, 23, 24, 28

Find the modal value of this dataset from its dot plot.

Work out the mean of this dataset: (-6), (-5), (-3), (-3), 1, 4, 5, 7 

Dataset A and dataset B both show the minimum temperatures in two different locations. How much bigger is the range of dataset A than the range of dataset B?

Summarising data

Lesson outcome