National Curriculum links

Statistics (Year 6): calculate and interpret the mean as an average. Statistics (Year 6): interpret and construct pie charts and line graphs and use these to solve problems. Statistics (Years 4 and 5): interpret and present discrete and continuous data; solve comparison, sum and difference problems using information presented in graphs and tables.

Key Stage 2 Mathematics programme of study, National Curriculum in England (Department for Education). Median, mode and range extend pupils towards the Key Stage 3 statistics objectives.

Learning objectives

By the end of the sequence, pupils will be able to:

  • calculate the mean of a set of data;
  • find the median, mode and range of a set of data;
  • present data in a bar chart and read values from it;
  • compare two sets of data and explain which average best represents them.

Lesson outline

Starter

Recap the mean: add the values and divide by how many there are. Work through a small example together so the method is secure before pupils handle real numbers.

Main activity

Pupils collect a real data set. Choose one of two contexts:

  • Elevation: use the elevation comparison tool to record the height above sea level of eight places of the pupils' choosing.
  • House prices: use the house prices by postcode tool to record the price of several recent sales in an area.

With their data set, pupils calculate the mean, find the median (the middle value when ordered), the mode (the most common value) and the range (largest minus smallest). They then present the data as a bar chart. As a discussion point, introduce why the median can be a fairer average than the mean when one value is unusually large, for example a single very expensive house, which is a powerful, real example of an outlier.

Plenary

Pupils collect a second, contrasting data set, for example a hilly area versus a flat one, or an expensive area versus a cheaper one, and compare the two using their averages and range. Which area is higher on average? Which has the bigger spread?

Differentiation

Support and challenge

  • Support: provide a smaller data set of friendly numbers and focus on the mean and range, with calculators available.
  • Challenge: calculate all four measures, identify any outliers, and explain in writing why the mean and median differ for a skewed data set.

Key vocabulary

data, data set, average, mean, median, mode, range, outlier, spread, bar chart.

Assessment: key questions

  • Can pupils calculate the mean accurately?
  • Can pupils find the median, mode and range of a data set?
  • Can pupils explain why the mean and median can differ, and which is fairer for their data?

Tools and links for this lesson