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Is anyone average?

By David, 26 November 2013 Activity

You will need

A screen grab from the CensusAt Schhol random sampler.The mouse cursor is hovering over the 'accept' button.

Click through to get to the data.

  • Internet access
  • Spreadsheet software such as Microsoft Excel or Open Office

To get the data

  1. Get online and visit the CensusAtSchool random sampler. This page will provide responses from a survey called CensusAtSchool. Read the conditions of use and if you agree, then click through to the next page.
  1. Select the following data options:
  • Reference Year – 2013
  • Questions to display – Select data by question

For ‘data by question’, check the following boxes:

  • Q8. Eye colour
  • Q17. Favourite take-away

    To make the columns the right width, double click on the lines in between the alphabet cells at the top.

    To make the columns the right width, double click on the lines in between the alphabet cells at the top.

  • Q20. Getting to school

Scroll down further and select the following data options:

  • Sample Size – 100
  • Postcode range – 0000 to 9999
  • Select by state/territory – All states/territories
  • Select year levels – choose your year level
  • Select sex – All

Press Get Data Sample at the bottom of the page.

  1. Click on the link next to ‘Download data.xls sample file’ at the bottom of new page. Open this file with your spreadsheet software.

    A spreadsheet. a lot of cells are highlighted - they all say 'hazel'. a menu has popped up and the 'fill' command is highlighted.

    To change the colour of cells, select them, right click and choose the background fill option.

To use the data

  1. When you open the file, you’ll have a table containing three columns and one hundred rows of information.
  2. Each column contains answers to one question. The first column, Q08.ColrEye, tells you a person’s eye colour. Q17.TAFood is their favourite take-away food, and Q20.TrvToScl tells you how they get to school.
  3. Each row contains all the answers to the survey by one person. We don’t know their name, but we can learn lots of other things about them by reading the answers for each question.
  4. If you’ve never used a spreadsheet before, follow this link to read some spreadsheet tips and tricks.

Exploring averages

In Excel 2007, there's only one drop-down menu in the sort command.

In Excel 2007, there’s only one drop-down menu in the sort command.

  1. Sort the rows by clicking on one entry in the first column, then clicking data > Sort. Choose the column you want to sort in the first drop-box (there might be other drop-boxes depending on the software you are using) and then press OK.
  2. Go to column A – Q08.ColrEye. Find the most common eye colour, and count the number of people with that eye colour.
  3. Now look at column B – Q17.TAFood. Work out how many people gave the most popular answer (hint – do another sort, and make sure you select Q17.TAFood in the first drop-box).
  4. Count up the number of people who have the most popular eye colour, and also take the most popular transport to school.
  5. Look at column C – Q20.TrvToScl. Find the most popular answer and count the number.

    The OpenOffice Calc sort command box. The first menu ays 'Sort by' and then has a drop down menu with the nemes of each of the columns.

    In Open Office, there are several drop down boxes – you only need to change the first one.

  6. Work out how many people are in the most popular group for all three answers.
  7. As each new mode is found, what happens to the number of members in the group that display all of the average characteristics? Given that there are 31 questions in the CensusAtSchool survey for 2013 do you think anyone is average for every single one?

What’s happening?

To make an average, you need to collect different information about one question. The average you find is a summary statistic about that group.

If you highlight all the most popular responses it's easy to see how many people have all three.

If you highlight all the most popular responses it’s easy to see how many people have all three.

But the average answer doesn’t necessarily tell you exactly what most people are like. For instance the 2011 CensusAtSchool data found that the most popular sport was netball. However, less than half the respondents chose it as their favourite sport, which means most people chose other sports. So the average for this question, in this survey, only tells you something about a large minority.

Numerical data, such as height, can be even trickier. If you measured the height of every person in your class very accurately, you’d probably find that they were all slightly different heights. That would mean at most, only one person could be exactly the average height!

An average is a summary of a lot of information, but it can’t tell you everything about a population. Being different from the average is normal, and in a lot of cases, very likely.

This activity used data from the 2011 and 2013 CensusAtSchool questionnaires.

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