Chapter 4: Measures of Central Tendency
Student Resources
I use the 4 “P’s” framework to help you learn the material in this chapter: Prepare, Practice, Participate, and Perform. To increase the chances to succeed in this course, I strongly encourage you to complete all four “P’s” for each chapter.
1 Prepare
1.1 Chapter Overview
This chapter covers measures of central tendency—the mode, median, and mean. These statistics help us identify the “typical” or “central” value in a dataset, which is essential for describing and comparing groups in movement science research.
1.2 Multimedia Resources
The following table provides access to video and slide resources for this chapter. Click the links to open them in an overlay for better viewing on all devices.
| Resource | Description | Link |
|---|---|---|
| Long Video Overview | A detailed video explaining the key concepts of mode, median, mean, and how to choose the right measure of central tendency. | 🔗 Watch Video |
| Slide Overview PDF | PDF slides that serve as an overview of this chapter. Read these before the textbook to introduce the main concepts and vocabulary. | 🔗 View Slides |
| Slide Deck HTML | Interactive HTML slides for class. During class, the instructor controls the presentation; after class, review at your own pace. | 🔗 Open Slides |
| Slide Deck PDF | PDF version of the slide deck for download and offline viewing. | 🔗 Download PDF |
1.3 Read the Chapter
Read (Weir & Vincent, 2021, p. Ch4) and (Furtado, 2026, p. Ch5) - optional but recommended - to understand mode, median, mean, and when to use each measure of central tendency.
To succeed in this course, you must read the textbook chapters assigned for each topic. This is the only way to learn the material in depth.
Once done, proceed to the next section to practice what you learned.
2 Practice
Practicing what you learned in the chapter is essential to mastering the material. Below are some resources to help you practice the material in this chapter.
2.1 Frequently Asked Questions
Measures of central tendency are statistics that identify a single value that represents the center or typical score in a distribution. The three main measures are the mode (most frequent value), median (middle value), and mean (arithmetic average).
Use the mode when: - You have nominal (categorical) data - You want to identify the most common or popular value - You’re interested in the most typical category The mode is the only measure of central tendency appropriate for nominal data.
Use the median when: - You have ordinal data or skewed distributions - There are extreme outliers that would distort the mean - You want a value that represents the “middle” of the dataset The median is resistant to outliers and works well with non-normal distributions.
Use the mean when: - You have interval or ratio scale data - The distribution is roughly symmetric (not heavily skewed) - You plan to use the data in further statistical calculations The mean is the foundation for many advanced statistics but is sensitive to outliers.
The mean is calculated using all values in the dataset, so extreme scores (outliers) can pull it away from the center of most of the data. For example, if most athletes run the 100m in 11-12 seconds but one runs it in 20 seconds, the mean will be higher than most individual times.
The mean is the arithmetic average (sum of all values divided by the number of values). The median is the middle value when data are arranged in order. In symmetric distributions, they’re similar. In skewed distributions, the mean gets pulled toward the tail while the median stays near the center of the data.
To calculate the mean: 1. Add up all the values in your dataset 2. Divide by the number of values Formula: \(\bar{x} = \frac{\sum x}{n}\)
To find the median: 1. Arrange all values in order from smallest to largest 2. If you have an odd number of values: the median is the middle value 3. If you have an even number of values: the median is the average of the two middle values
Distribution shape refers to how data are spread out—symmetric, skewed left, skewed right, or multimodal. It matters because the shape tells you which measure of central tendency is most appropriate and helps you interpret your data correctly.
In a right-skewed (positively skewed) distribution: - The mode is at the peak (lowest value) - The median is in the middle - The mean is pulled toward the long right tail (highest value) Order: Mode < Median < Mean
2.2 Test your Knowledge
Take this low-stakes quiz to test your knowledge of the material in this chapter. This quiz is for practice only and will help you identify areas where you may need additional review.
3 Participate
This section includes activities and discussions that will be completed during class time. Your active participation is essential for deepening your understanding of the material.
During class, we will: - Calculate and compare measures of central tendency for real movement science data - Analyze distribution shapes and discuss their implications - Work through examples of choosing appropriate measures for different data types - Discuss how outliers affect different measures of central tendency
4 Perform
4.1 Apply Your Learning
Now that you’ve prepared, practiced, and participated, it’s time to demonstrate your mastery of the material through assignments and assessments.
I strongly encourage you to complete the previous “Ps” (Prepare, Practice, Participate) before attempting any assignments or assessments associated with this chapter.
4.2 Lab Assignment
Complete Lab 1: Central Tendency and Variability to apply what you’ve learned about measures of central tendency (mode, median, mean) and variability (range, variance, standard deviation).
- Download the Word document above (click to open, then save to your computer)
- The document has two parts:
- Part 1: Instructions - Read this section for assignment details, grading rubric, and resources
- Part 2: Your Answers - Complete all questions in this section
- Complete all questions in Part 2 using SPSS to analyze the Core Dataset
- Include your SPSS outputs by pasting as images or tables
- Delete Part 1 (Instructions) before submitting - submit only Part 2 (Your Answers)
- Submit your completed lab via Canvas
Note: This lab integrates concepts from both Chapter 4 (Central Tendency) and Chapter 5 (Variability), as these concepts should be reported together in practice.