All Activities
Maths

Mean, Median and Mode in Context

Overview

Students work with realistic data sets to understand that different averages tell different stories, and practise choosing the most appropriate one.

Learning Objective
Students calculate the mean, median, and mode of data sets and decide which average is most useful for a given real-world context.

Resources needed

  • Mini whiteboards
  • Data sets on board or printed

Lesson stages

0 / 7 done
  1. 1 Display: salaries at a small company: £18k, £19k, £20k, £21k, £22k, £22k, £80k (the owner). 'What is the average salary?' Different students may get very different answers — introduce that there are three types of average.
  2. 2 Mode = most common value. In the salary data: mode = £22k. 'This appears twice — it is the most frequent.' Note: there can be more than one mode, or no mode.
  3. 3 Median = middle value when ordered. The data is already ordered. There are 7 values — the middle is the 4th: £21k. 'If there is an even number of values, we average the two middle values.'
  4. 4 Mean = total ÷ number of values. Total = 18+19+20+21+22+22+80 = 202. Mean = 202÷7 ≈ £28.9k. 'The mean is much higher because the owner's salary pulls it up — this is called an outlier.'
  5. 5 'If you were applying for a job here, which average would give you the most realistic expectation?' (Median or mode.) 'If you were the owner trying to show the company pays well?' (Mean.) Discuss how averages can be used selectively.
  6. 6 Students calculate mean, median, and mode for three different data sets: test scores, shoe sizes, temperatures. For each, they state which average is most appropriate and explain why.
  7. 7 Students create a data set of 7 values where the mean and median are different, and explain why they differ.

Tap a step to mark it as done.

Variations

  • Extend to grouped frequency tables for calculating estimated mean
  • Compare two groups using averages (e.g. boys vs girls test scores)
  • Use spreadsheet software to generate instant averages
More information

Display: mean (add all, divide by count), median (middle value, ordered), mode (most frequent). Use sentence frames: 'The most appropriate average here is ___ because ___.'

Provide a step-by-step guide for each average with a worked example. Reduce data sets to 5 values for those needing support.

Do students order data before finding the median? Do they divide by the correct count for the mean? Can they justify which average is most appropriate?

All data sets can be displayed on the board. No printed materials needed. Students work on mini whiteboards.

Students often forget to order the data before finding the median, or find the middle position rather than the value. Reinforce: order first, then count to the middle.

Activity details
Primary Medium 40 minutes 5 minutes prep Solo, Pairs Indoor
Topics
Mean Median Mode Statistics Averages