The average kid

One topic that students in middle school are likely to find interesting is themselves. This activity touches on almost all the outcomes for each grade level (with appropriate modifications) with a long term, whole class project. All you need to do to introduce the project is to suggest that they are going to find out about themselves, by trying to create a composite average kid in their class. (SCOs 4-F8, 5-F7, 6-F9, etc.)

Stage 1: The average kid in the class.

Part a: collecting the data

It is important that students understand that there are many ways to collect data, and that different ways of collecting the data can lead to different results. For instance asking an open question about each student's favourite food is likely to result in many different answers, making it difficult to say that a significant number like a particular food. On the other hand asking them to select their favourite food from a list of five choices will be more likely to produce a clear winner. Leading questions should also be discussed. (SCOs 4-F1, 6-F1,F2)

As a class brainstorm things that they would like to know about themselves and each other. It may be appropriate during this discussion to raise the issue of questions that may produce misleading results because people are likely to give incorrect answers, either because they misunderstand the question (The question Favourite beetle may be misheard as Favourite Beatle) or because the questions is potentially embarrassing or incriminating (Have you ever stolen from a classmate?).

Assign individuals, pairs or groups the task of writing the exact question they will ask to find out one of the things they'd like to know. Either collect these and edit them yourself (taking the opportunity to note the sophistication of the students understanding of the importance of asking clear, non-leading questions), or have them exchange them for peer editing.

Once the questions are designed, each individual, pair or group should survey the class, collecting the data for their question.

Part b: Analysing the data

Make sure the class understands the difference between categorical data (e.g., birth month), ordered data (e.g., rate your happiness on a scale of 1-5), and numerical data (e.g., height). Assess this by having each individual, pair or group classify the data they have collected.

The first step in the analysis is describing the results using measures of central tendency (averages) and measures of dispersion (how spread out it is). Define the three measures of central tendency (mean, median, mode) and as a class discuss how to make a table (see below) showing which measures can be used for each type of data. Also define “maximum”, “minimum”, “range” and “frequency” and discuss what kinds of data they could describe.  Have each individual, pair or group describe their results appropriately.  In some cases two averages might be useful, especially if there are outliers in the data.  In that case the effect of omitting the outlier should be discussed. (SCOs 4-F2,F7, 5-F6, 6-F8).

Discuss as a class what types of graph would be best to display their data. Add a row to your table to show which graph types are best suited to which types of data. Grade 5 and 6 students may want to separate boys and girls and display the results using double bar graphs.  Have each individual, pair or group make two graphs of their data.  (SCOs 4-F5, 5-F1,F2,F4, 6‑F4,F5)

Part c: reporting the data

Based on their analysis, have each individual, pair or group prepare a report to the class describing that they would say is the average answer to their question. Questions from the other members of the class should be encouraged. (SCOs 4-F3,F6, 5-F4,F1,F2 6‑F4,F5,F7)

The class may want to make a bulletin board display showing their charts and a scale model of their average kid (or average boy and girl).

A follow-up activity would be to consider whether some responses are related to others (e.g., shoe size and height). Scattergraphs can be used to explore this question (SCOs 6-F3,F6)

Stage 2

For a grade 6 class this stage should be done. For younger grades it is optional.

Raise the question of whether their averages would be reasonable answers to the question of what the average kid of their age in the school, or larger area, is like. This leads to a consideration of sampling, and what factors make a sample a good one. If their are clear differences between classes in the school or schools in the area (e.g., a French immersion class, or an urban/suburban/rural split), this would suggest that their sample cannot be generalised. (SCO 6-F1,G2).

Repeat the three parts of Stage 1 using a larger sample (all the grade n classes in the school, or link with another school and exchange data).  Compare the results and discuss the accuracy of their sampling now with this larger data set.  How far can they generalise now?

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