Contextualization

Theoretical Introduction

The Median is one of the most common measures of central tendency in mathematics and statistics. It represents the value that separates the larger half from the smaller half of a data set. It is especially useful when dealing with large data sets, where it can be difficult to determine what would be a 'typical value'. The median is determined by organizing the data in ascending or descending order and identifying the value that is in the middle.

In contrast to the mean, the median is not skewed by extremely high or low values (outliers) that can affect the average of a set. Therefore, the median is a more robust representation of a 'typical value' in many data sets.

Remember that when the data set has an odd number, the median is the value that is in the middle. But when the data set has an even number, the median is the average of the two values that are in the middle.

Contextualization

The Median, as a measure of central tendency, has a variety of real-world applications. It is commonly used in the field of economics to determine average salaries. Instead of just using the mean, which can be inflated by a small number of extremely high salaries, the median is often used to provide a more accurate view of the common salary.

In life and health sciences, the median is often used in studies to prevent outliers from distorting the interpretation of data. For example, in a study on sleep duration, if one person sleeps 15 hours per night and everyone else sleeps between 6 and 8 hours, the median will provide a more accurate representation of the 'typical' sleep duration.

Practical Activity

Activity Title: Learning Median through the Real World

Project Objective

The objective of this activity is to apply the concept of median in a real-world scenario. Students will conduct a survey among their classmates, collect the responses, and then organize the data and calculate the median. This project will involve teamwork skills, field research, data organization, and mathematical calculations.

Detailed Project Description

Each group will choose a theme related to the daily life of students, such as the number of hours of study per day, the number of books read in the last month, or the average duration of nighttime sleep, for example. The groups will conduct a field survey among the students at school or in the community, collect the data, and organize it in a table.

After collecting the data, students will be challenged to calculate the median. They should also calculate the mean and understand the difference between these two concepts. The result should be presented in a graph, where they can visualize the median, the mean, and how the data is distributed around these measures.

Required Materials

• Paper and pen for the survey
• Calculator
• Computer with spreadsheet software (such as Excel or Google Sheets) for data organization and calculations
• Chart creation application or spreadsheet software to visualize the data

Detailed Step-by-Step

1. Form groups of 3 to 5 students.

2. Choose a theme for the survey related to the daily life of students.

3. Create a simple questionnaire to collect the necessary information.

4. Establish a plan to collect the responses (for example, during breaks, in the school library, etc).

5. Conduct the survey and collect the data.

6. Organize the data in a spreadsheet.

7. Calculate the median and mean of the collected data.

8. Create a graph representing the data collected and where the median and mean can be visualized.

9. Prepare a report containing the introduction (context and project objective), development (description of the methodology and presentation of results), and conclusion (learnings and conclusions drawn from the project).

Project Deliverables

After following the detailed steps above, each group should deliver 1) the spreadsheet with the collected data and the median and mean calculations; 2) the graph representing the data, the median, and the mean; and 3) the written report.

In the report, students should write the Introduction describing the chosen theme, its relevance to daily life, and the application of the concepts of median and mean. In the Development section, they should describe the methodology used for data collection, explain in detail how the calculations were performed, and discuss the results obtained. In the Conclusion, students should summarize the main points of the project, highlight the learnings obtained, and draw conclusions on the theme. Finally, the Bibliography, where they should indicate the sources used during the project development.