Comparing Data Distributions

'Whose results are best? Boys, Girls, Monkeys, Martians, Flying pigs, Babies or Robots?' 

All of the above species were asked to take a multiple choice mathematics test and the results were recorded. Now it is up to us to decide how the species compared to each other! This exercise is all about looking at the subtle differences between data sets. What do they have in common? Where are they different? There are lots of answers to both of those questions. There are lots of different ways to approach this task and your teacher will help you decide how. You will need to calculate averages and measures of spread/dispersion. More importantly, you will need to think about what these tell us about the different species and how they can be used to compare them! This can be done on paper, with a calculator or using computers. Which ever way you do it, there are lots of surprises and 'Who is the best?' becomes a very difficult question to answer! Good luck!


The aim of this activity is for students to think critically about interpreting data and their calculations. The activity involves the calculation of measures of central tendency and dispersion. It involves the production of measures of box plots. Students have to identify the key differences between the data sets amongst that which they have in common.


As suggested above, there are a number of ways to approach this task. The resources are below.

The most open approach to this task is to start with just the data and do your own analyses from scratch!

 The Data - This is the seven data sets you need to do the analyses.

Otherwise, or as well, you can do these matching activities to help you unlock the secrets in the data.

 Match the box plots and histograms - In this task you must match a box plot and a histogram to each of the data sets.

 Match the descriptions - In this task, a summary analysis of each species is given and your job is to match it to the correct species.

Teachers will need to think briefly about how they want to run this activity by reading the  Comparing Data Distributions - TN teacher notes

The Data

Here is a screen shot of the data you will be working with....

Syllabus Links

Measures of central tendency, measures of dispersion, box plots and comparing data distributions.

New - Sections 2.5 and 2.6 Previous - Sections 6.5 and 6.6


  • Students are presented with the data and the idea.
  • Teachers decide how they want students to approach the task.
  • Students can be presented with the raw data and asked to analyse, present and summarise.
  • Students can do the matching exercise with the box plots and histograms.
  • Students can do the matching exercise with the descriptions.
  • Any of the above work can be put together to make a display.
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Comments 2

Grant Fossum 3 November 2016 - 12:57

This is such a cool activity, I cannot wait to try it. Is the data suppose to indicate the number (percentage) of multiple choice questions they got right?

Jim Noble 6 November 2016 - 14:01

Yep, these are percentage scores. Glad you like it

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