Chapter 5: Measures of Variability
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 variability—statistics that describe how spread out or consistent values are in a dataset. You’ll learn about range, interquartile range, variance, standard deviation, and coefficient of variation, and understand when to use each measure.
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 measures of variability, range, variance, standard deviation, and when to use each measure in movement science research. | 🔗 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. Ch5) and (Furtado, 2026, p. Ch6) - optional but recommended - to understand measures of variability, range, variance, standard deviation, and coefficient of variation.
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
Variability is a measure of the spread or dispersion of data. It tells us how much scores differ from each other and from the central tendency. While measures of central tendency tell us where the center is, measures of variability tell us how tightly or loosely data cluster around that center.
Variability is important because two groups can have the same mean but very different spreads. For example, two training groups might both average 30 seconds for a sprint, but one group’s times might range from 28-32 seconds (low variability) while the other ranges from 20-40 seconds (high variability). This difference has important practical implications.
The range is the simplest measure of variability, calculated as the difference between the highest and lowest scores: Range = Highest − Lowest. It provides a quick estimate but is unstable because it depends on only two values and is heavily affected by outliers.
The interquartile range (IQR) is the difference between the 75th percentile (Q₃) and the 25th percentile (Q₁): IQR = Q₃ − Q₁. It represents the spread of the middle 50% of the data and is resistant to outliers, making it useful for skewed distributions.
Use IQR when: - You’re more interested in typical variability (middle 50%) than extremes - The data are ordinal - The distribution is highly skewed - There are extreme outliers IQR gives a more representative picture of variability for most of the data.
A deviation score is the distance of each raw score from the mean: d = X − X̄. Positive deviations indicate scores above the mean, negative deviations indicate scores below the mean. The sum of all deviation scores always equals zero.
Variance is the average of the squared deviations from the mean: V = Σ(X − X̄)²/N. It considers every score and provides the foundation for many statistical calculations. Because deviations are squared, variance is in squared units (e.g., cm²), which can be hard to interpret.
We square deviations to: 1. Eliminate negative signs (negative and positive deviations would cancel out) 2. Preserve information about distance from the mean 3. Make the math work properly for further statistical calculations Squaring is preferable to using absolute values for mathematical reasons.
Standard deviation (SD) is the square root of variance: s = √V. It’s in the same units as the original data, making it easier to interpret than variance. SD represents the typical or average distance of scores from the mean.
For population variance and SD, we divide by N (total number of scores). For sample variance and SD, we divide by n−1 (degrees of freedom). The n−1 correction provides an unbiased estimate when working with samples. Most research uses sample formulas.
Degrees of freedom (df) represent the number of values free to vary after certain constraints. For sample variance, df = n−1 because once we calculate the mean, only n−1 deviations can vary independently (the last one is determined by the constraint that deviations sum to zero).
The coefficient of variation (CV) expresses standard deviation as a percentage of the mean: CV = (s/X̄) × 100. It allows comparison of relative variability across different variables or measurements with different units or scales.
Standard deviation tells you the typical distance of scores from the mean. Small SD = scores cluster tightly (low variability). Large SD = scores spread out (high variability). For normal distributions, about 68% of scores fall within ±1 SD of the mean, and about 95% within ±2 SD.
An SD of zero means no variability—all scores are identical and equal to the mean. This is rare in real data and usually indicates a measurement or data entry problem.
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 different measures of variability - Interpret variability in the context of movement science research - Discuss when to use each measure of variability - Analyze real datasets and identify appropriate variability measures
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.