Contextualization

Theoretical Introduction

In this project, we will be exploring the world of 'Sampling Surveys'. So, what is a sampling survey? It is a method of collecting data and information from a selected part (the sample) of a larger group (the population). By selecting a sample, our goal is to obtain information that can be extrapolated to the entire population.

The main measures we can extract from a sampling survey are measures of central tendency: mean, median, and mode. The mean is the sum of the observations divided by the number of observations, the median is the middle value, and the mode is the most frequent value. These measures help us to have an overview of the data distribution.

Another important concept is the range, which is the difference between the maximum and minimum values of our data. It gives us an idea of how spread out our data is. The correct exploration of these concepts allows us to make coherent and accurate analyses about the population from the collected sample.

Contextualization

Sampling surveys are used in a variety of fields, from business to social sciences. If you have ever answered a customer opinion survey or a market research questionnaire, then you have participated in a sampling survey!

Such surveys are essential because it is not always practical or possible to collect data from everyone in a population. For example, if a company wants to know its customers' opinions about a new product, it would not be practical to ask all of them. Instead, they would select a sample of customers and use the responses to infer the opinions of all their customers.

Understanding and practicing these concepts are fundamental, for example, to understand how election polls, market studies, or scientific research in general are conducted. Therefore, learning to plan and conduct a sampling survey is not only important for your mathematical knowledge but also for your development as a conscious citizen.

Recommended Reading and Research

To deepen your understanding of these concepts, we recommend the following material:

• Book 'Estatística Básica' by Wilton Bussab and Pedro Morettin. This book is a reference for an introduction to Statistics and covers, in a didactic way, the relevant topics for this project.
• The website of the Brazilian Institute of Geography and Statistics (IBGE) IBGE Educa which has a section dedicated to statistical knowledge that is a valuable source of information and practical examples.
• The Khan Academy platform also has a vast and excellent material on the subject, specifically in the Statistics and Probability section.

Practical Activity

Activity Title: Planning and Execution of Sampling Surveys

Project Objective

Students will plan and execute a real sampling survey related to a topic of their interest, such as food, sports, video games, fashion, etc. Then, students should analyze the collected data, highlighting the measures of central tendency and range, and finally, write a report on the project.

Project Description

The project will be developed in groups of 3 to 5 students, and the estimated duration for the total completion of the project is one week or up to 4 hours per participating student. The project will be divided into four parts: research planning, data collection, data analysis, and report writing.

Necessary Materials

• Paper and pen for initial sketch and planning;
• Computer with internet access for research and questionnaire development, data collection and analysis, and report writing;
• Spreadsheet software (such as Microsoft Excel, Google Sheets, or similar);
• Software for online questionnaire development (such as Google Forms or similar);
• Text writing tool for report writing (such as Microsoft Word, Google Docs, or similar).

Step by Step

Part 1: Research Planning

1. Students must choose a topic of interest for the research.
2. Students must formulate the questions they want to answer with the research. The questions should be clear and should address the chosen topic meaningfully.
3. Students must decide on the type of sample they will collect (for example, simple random sample, systematic, or stratified sample) and justify their choice.
4. Students must create a questionnaire using the chosen online tool, according to the formulated questions.

Part 2: Data Collection

1. Students must distribute the questionnaire to the selected sample and collect the responses.

Part 3: Data Analysis

1. Students must compile the responses in a spreadsheet.
2. Students must calculate the measures of central tendency (mean, median, and mode) and the range of the collected data.
3. Students must create appropriate graphs to represent the data sets.

Part 4: Report Writing

1. Students must write a report containing: Introduction, Development, Conclusions, and Bibliography. The report should have the format of a scientific article.
2. Introduction: Students must contextualize the research topic, its relevance and real-world application, and the project's objective.
3. Development: Students must explain the theory behind sampling surveys, explain the activity in detail, indicate the type of sample used and the data collection methodology, present and discuss the results obtained, including the calculations of measures of central tendency and range and the representation of data in graphs.
4. Conclusions: Students must conclude the work by summarizing their main points, explaining the learnings obtained, and drawing conclusions about the project.
5. Bibliography: Students must indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.

At the end of this project, it is expected that students have acquired a practical understanding of how to plan and conduct a sampling survey, calculate and interpret measures of central tendency and range, and articulate their conclusions in a written report.