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.

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

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

Analysing different statistical representations

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

Summarising data

Changing a data point

Evaluating the range

Comparing statistical representations

Comparing summaries of data

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

Alex is taller than average because he is taller than the modal height.

Alex is taller than average because he is taller than the mean height.

Alex is shorter than average because he is shorter than the median height.

Alex is around average height because his height is close to frequent heights.

Alex is shorter than average because the maximum height is 150 cm

Which of these statements is valid when comparing the height of Alex in year 6 to the "average" height of other year 6s at his primary school?

Select the data sets which match the following statistical summary: a range of 14

Which of these is a representative median of the data set that has following statistical summary: a mode at 54, a range of 14, a mean of approximately 50?

Sam asks 55 people how many times per month they visit the supermarket. Sam loses some of the data, but represents the rest on a bar chart. How many people's data did Sam lose? {{ }} people

Here is an incomplete bar chart for a data set. The range of the data set is 12 days. What is the maximum number of days per month that the people surveyed visited the supermarket? {{ }} days

This bar chart has missing bars. 50 people were surveyed. The range is 7. The frequency of 11 days is 3 greater than the frequency of 10 days. Work out the frequency for 10 days.

In which of these statistical graphs can the frequency of the data set be seen from the graph alone?

Which of these statistical graphs is best at showing the change in the value of something over time?

Which of the following statements is true when describing the mode of these four bar charts?

Match the statements that summarise these bar charts to the value that end each sentence.

How much larger is the mode of this dot plot compared to its mean? {{ }}

How much larger is the mean of this dot plot compared to its mode? Give your answer rounded to 1 decimal place. {{ }}

Analysing different statistical representations

Lesson outcome