Context

Median is a very important measure of central tendency in Statistics. Imagine a set of data arranged in an orderly list. In the middle of that list you will find a value called Median. This is the midpoint value, which divides the list exactly in half. If your data has an odd number of entries the Median will be the middle value. If it's even, it will be the average of the two middle numbers.

For example, let's say you have the grades for five students in one test: 5, 6, 7, 8 and 10. The Median is 7 because that's the value in the exact middle. Now, let's say you have six students and the grades are: 5, 6, 7, 8, 10 and 10. In this case, the middle two values would be 7 and 8, and so the Median is 7.5.

Median is significant because it gives you an idea of "typicalness" in a data set. It shows where the center, or the most typical, values in a data set lie. Median has real world uses in many different fields, from economics all the way to life science. In economics, for instance, it is used to calculate the average income in a country, which helps to understand the distribution of wealth.

Median is a middle position measure that provides an idea of the "typical" value in a data set. When analysing data, the Median can often give you a clearer picture. It tends to be less affected by outliers, or non symmetrical distribution than the Mean is.

For further background on this subject, students may rely on the "Statistics handout", found here, in Portuguese; and "Measures of central tendency: mean, median and mode" here, also in Portuguese, as good references for discussion and study.

Hands on exercise: "Measuring Median"

Objective

This project is meant to give students an hands on, real world, understanding of Median. They'll gather data, analyse it and draw meaningful conclusions about the topic of their choosing.

Description

Divide the class in 3-5 people groups and have them pick a topic they'd like to work with. They can go for anything from average household income in their country to the amount of time students in the school spend doing homework. They'll collect a set of data on the topic, then they will need to find the Median of the set.

Material

• Notebooks or loose sheets of paper
• Pencils and pens
• Calculator
• Computers with Internet access (optional, to research the topic)

Steps

1. Group creation and topic selection: Have the students organise themselves in groups of three to five members each and select a topic they all agree to work with.

2. Data gathering: The groups now have to find the information that will allow them to calculate the Median on the chosen topic. For instance, if their topic is "Average income in our town" the groups will need to do research on the incomes in their area to find the necessary information to do their job

3. Median calculation: With the data in hand the students now order it and find the Median value

4. Analysis and results interpretation: Now that they have the Median number, they need to analyse and understand what that result represents regarding the topic of the group's choosing

5. Documentation: The groups will now create a report that includes:

   • Introduction: presenting the chosen topic, explaining the importance and purpose of calculating Median for the chosen theme.
   • Development: a description of the theory of the Median, how the data was gathered, analysed, the presentation of the data set, the Median and its meaning.
   • Conclusion: a resume of the most significant points, the lessons learned and conclusions regarding the project
   • Referrals: the sources consulted to complete this work.

This project is to be completed in a week and all members are expected to be ready to present both the development and conclusions for it. They are also required to demonstrate teamwork, time management, problem solving and communication abilities.