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

Checking understanding of the mean

Maths

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

The frequency is the number of times an event occurs; or the number of individuals (people, animals etc.) with some specific property.

The sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.

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

Calculating the mean

the central (middle) piece of data when the data is in numerical order. A measure of central tendency representing the average of the values

Understanding the median

Calculating the median

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

Sets of data which have two modes are known as bimodal data

Understanding the mode

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

Calculating the mode

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

The spread/dispersion of data values describes how far apart the pieces of data are.

Understanding and calculating the range

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

Sets of data which have two modes are known as bimodal data.

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

The mode is the most frequent value in a dataset.

Changing a data point

A data point that is extremely large or small compared to the rest of the dataset.

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

Describes how far apart pieces of data in a dataset are.

Evaluating the range

A pie chart (pie graph) is a circular graph where sectors represent different groups proportionally.

A bar chart (bar graph) is a graph consisting of bars visually representing the frequency of objects or groups.

Comparing statistical representations

is a summary measure that attempts to describe a whole dataset with a single value that represents the middle or centre of its distribution.

Comparing summaries of data

A statistical summary sums up the features of a data set. It may contain the averages (mean, median, mode). It may also contain the range.

Analysing different statistical representations

Correlation describes the extent to which the relationship is close to a linear relationship.

Correlation

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

Bias can be present in any sample collected from a population and may affect the results of a statistical investigation

Statistical problems - data collection

A statistical summary sums up the features of a data set.

a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution

Statistical problems - statistical summaries

A pictogram (pictograph) is a graph consisting of pictures to visually represent the frequency of objects or groups.

A visual representation for bivariate data. It can be useful when determining the nature of the relationship between two variables

A bar chart (bar graph) is a graph consisting of bars visually representing the frequency of objects or groups

Statistical problems - data presentations

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

Bias can be present in any sample collected from a population. e.g. only asking year 7 pupils about a whole school issue.

A statistical summary sums up the features of a data set

Statistical problems - drawing conclusions

A summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution

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

Numerical summaries of data

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These lessons will be removed by end of Summer Term 2025.