Real-world examples of examples of measures of variability

Starting with real examples of measures of variability

Let’s skip the dry definitions and go straight to concrete situations. Here are a few real examples of examples of measures of variability that show up in everyday life:

• A teacher comparing how consistent two classes are on a math test.
• A hospital tracking how much patients’ blood pressure readings fluctuate.
• An HR manager comparing salary inequality across departments.
• An investor checking how risky different stocks are.
• A basketball analyst judging which player is more consistent game to game.

In every one of these cases, an average alone is misleading. Two groups can have the same mean but wildly different spreads. That’s exactly what measures of variability are built to capture.

Range: the simplest example of spread

If you want the fastest example of a measure of variability, start with the range: the difference between the largest and smallest values.

Classroom test score example

Imagine two algebra classes take the same test, scored out of 100.

• Class A scores: 70, 72, 75, 76, 77, 78, 79, 80, 81, 83
  • Minimum = 70, Maximum = 83 → Range = 13
• Class B scores: 40, 55, 60, 70, 80, 85, 90, 92, 95, 100
  • Minimum = 40, Maximum = 100 → Range = 60

Both classes might have similar average scores, but the range shows a big difference in variability. Class B has students who are really struggling and others who are acing the test. Class A is much more tightly clustered.

This is one of the best examples of how a simple measure of variability can tell a more complete story than the mean alone.

Weather temperature example

Think about daily high temperatures in two cities over a week in March:

• City 1 (mild): 58, 60, 61, 59, 60, 62, 59°F → Range = 62 − 58 = 4°F
• City 2 (wild): 40, 47, 55, 65, 72, 50, 44°F → Range = 72 − 40 = 32°F

Same country, same season, completely different variability. Even this simple example of a measure of variability tells you City 2’s weather is far less predictable.

Range is intuitive, but it’s sensitive to outliers. That’s why statisticians like to add more refined measures of variability to the toolbox.

Variance and standard deviation: the workhorses of variability

When you hear analysts talk about “volatility” or “spread,” they’re usually talking about variance or standard deviation.

• Variance: average of the squared distances from the mean.
• Standard deviation (SD): square root of the variance, back in the original units.

These two are the classic examples of measures of variability used in science, finance, and social research.

Salary inequality example

Consider two departments at a tech company. Both have an average salary of $80,000, but the pay structures are very different.

• Department A salaries (in $1,000s): 75, 78, 79, 80, 81, 82, 85
  • Very tight cluster around 80.
• Department B salaries (in $1,000s): 40, 55, 65, 80, 95, 110, 135
  • Some people earn much less, others far more.

Both departments have the same mean, but Department B has a much higher standard deviation. That higher SD is a numerical example of pay inequality.

This kind of analysis shows up in labor economics and policy all the time. For instance, the U.S. Bureau of Labor Statistics regularly reports distributions of wages, not just averages, to capture variability across workers.

Stock market volatility example

Investors live and die by standard deviation. Suppose you track the daily returns of two investments over a month:

• Fund X: returns hover between −0.5% and +0.7% most days.
  • Low standard deviation → relatively stable.
• Fund Y: swings between −3% and +4% on a regular basis.
  • High standard deviation → much more volatile.

Even if both funds have the same average return, the higher standard deviation of Fund Y signals higher risk. This is one of the classic real examples of examples of measures of variability in finance.

If you want a formal reference, the concept of volatility as standard deviation is central in modern portfolio theory and is covered in many university finance courses (for example, materials from MIT OpenCourseWare).

Blood pressure in clinical research

In medical studies, researchers don’t just report the average blood pressure; they almost always add a standard deviation. For example, a study might say:

Mean systolic blood pressure = 128 mmHg, SD = 9 mmHg (n = 600)

That SD of 9 tells you most patients are fairly close to the mean. If the SD were 25, the group would be far more heterogeneous.

Organizations like the National Institutes of Health routinely use standard deviation in their published research to show how much patient data vary around the average.

Interquartile range: variability without the outliers

The interquartile range (IQR) is the distance between the 25th percentile (Q1) and the 75th percentile (Q3). It’s a favorite when you want examples of measures of variability that ignore extreme outliers.

Emergency room wait time example

Imagine an ER tracks patient wait times (in minutes) over a day:

5, 7, 8, 10, 12, 15, 16, 18, 20, 22, 25, 27, 30, 120

That 120-minute wait is an outlier (maybe a rare, complex case). The range is 120 − 5 = 115 minutes, which makes the ER look worse than it typically is.

Now look at quartiles:

• Q1 (25th percentile) ≈ 10 minutes
• Q3 (75th percentile) ≈ 25 minutes
• IQR = 25 − 10 = 15 minutes

That IQR says that the middle 50% of patients wait between about 10 and 25 minutes. For hospital administrators, this is a more realistic example of performance than the raw range.

The Centers for Medicare & Medicaid Services and other agencies often publish hospital quality metrics that rely on distributions, not just single-point averages, because variability directly affects patient experience.

Household income distribution example

Household income is famously skewed by very high earners. If you want real examples of measures of variability that are less distorted by billionaires, you look at the IQR.

Suppose in a region you have:

• Q1 income = $40,000
• Median income = $60,000
• Q3 income = $90,000
• IQR = $50,000

That IQR tells you that the middle half of households earn between \(40k and \)90k. Two regions can have the same median income but very different IQRs, signaling very different levels of economic spread.

Mean absolute deviation: a more intuitive spread

The mean absolute deviation (MAD) is the average of the absolute distances from the mean. It’s often easier to explain than variance because you’re not squaring anything.

Student performance consistency example

A teacher wants to know which student is more consistent across five quizzes, each scored out of 10.

• Student 1 scores: 7, 7, 8, 8, 8

  • Mean = 7.6
  • Absolute deviations: 0.6, 0.6, 0.4, 0.4, 0.4 → MAD ≈ 0.48

• Student 2 scores: 5, 7, 7, 9, 10

  • Mean = 7.6
  • Absolute deviations: 2.6, 0.6, 0.6, 1.4, 2.4 → MAD ≈ 1.52

Same mean, but Student 2 has a much higher mean absolute deviation. This is a clean example of a measure of variability showing that Student 2 is less predictable.

Teachers and education researchers sometimes prefer MAD when explaining variability to students because it lines up with the intuitive idea of “average distance from the center.” For instructional materials, sites like Khan Academy provide visual and numerical examples of MAD.

Putting it together: comparing measures with real examples

Let’s pull these ideas into a single scenario and see how different measures behave.

Sports performance example

Two basketball players, Alex and Jordan, both average 20 points per game over 10 games.

• Alex’s points: 18, 19, 20, 20, 21, 19, 20, 21, 20, 22

  • Range: 22 − 18 = 4
  • SD: small (scores tightly clustered)
  • IQR: narrow (middle games close together)

• Jordan’s points: 5, 8, 12, 18, 20, 23, 28, 32, 35, 41

  • Range: 41 − 5 = 36
  • SD: large (huge game-to-game swings)
  • IQR: much wider

Same average, totally different story. The best examples of examples of measures of variability are exactly like this: they show you that the mean can be identical while the risk, reliability, and predictability are not.

Coaches might prefer Alex for steady performance, while fans might love Jordan’s explosive, high-variance style. The choice depends on how you feel about variability.

Public health example: BMI distributions

Public health agencies care a lot about the distribution of health measures, not just the average. Take body mass index (BMI) in a population:

• Population A: Mean BMI = 26, SD = 2
  • Most people are near the mean.
• Population B: Mean BMI = 26, SD = 7
  • Many more people at both very low and very high BMIs.

Both populations look the same if you only glance at the mean. But the higher standard deviation in Population B signals more people at higher risk categories. Institutions like the Centers for Disease Control and Prevention routinely analyze not just average BMI, but the full distribution, because variability affects rates of diabetes, heart disease, and other conditions.

This is one of the best real examples of examples of measures of variability actually driving policy: how spread-out health metrics are can influence screening guidelines, resource allocation, and prevention strategies.

Why multiple measures of variability matter in 2024–2025

In modern data work—whether you’re looking at climate trends, social media metrics, or pandemic data—using a single average is asking to be misled. Some of the strongest examples of measures of variability today come from:

• Climate data: Meteorologists track not just average temperatures, but the variability of heat waves, cold snaps, and rainfall. A city with the same average temperature as another can have far more extreme days.
• Epidemiology: During disease outbreaks, researchers look at variability in case counts across regions and time. High variance can signal hotspots or super-spreading events.
• Online behavior: Platforms analyze the spread of session lengths, click-through rates, and engagement. Averages can hide the fact that a small group of users behaves very differently from the rest.

Data science in 2024–2025 is increasingly about understanding distributions, not just single summary numbers. The best examples include companies and public agencies that explicitly publish standard deviations, IQRs, and other measures alongside the mean.

Quick recap: examples of examples of measures of variability

To keep this grounded, here’s how you might match situations to specific measures:

• Range: Quick snapshot of spread; good for a first pass, but sensitive to outliers.
  • Example of use: comparing the spread of test scores across two classes.
• Variance & standard deviation: Workhorses for most statistical models and risk analysis.
  • Examples include: stock volatility, variation in blood pressure, salary dispersion.
• Interquartile range (IQR): Great when outliers distort the picture.
  • Real examples: ER wait times, income distributions, skewed health measures.
• Mean absolute deviation (MAD): Intuitive measure of average distance from the mean.
  • Example of use: explaining consistency in student performance.

When you read research, policy reports, or financial analysis, look for these. If you only see an average, you’re missing half the story.

FAQ: short answers with examples

What are some common examples of measures of variability?

Common examples of measures of variability include range, variance, standard deviation, interquartile range (IQR), and mean absolute deviation (MAD). In practice, you’ll often see standard deviation reported in scientific papers, IQR in boxplot summaries and skewed data, and range in quick descriptive summaries.

Can two datasets have the same mean but different variability?

Yes, and this is one of the most important examples of why variability matters. Two groups of salaries, test scores, or health measurements can share the same mean but have very different standard deviations or IQRs, leading to very different interpretations about risk, inequality, or consistency.

Which example of a measure of variability is easiest to explain to beginners?

Range is usually the easiest example of a measure of variability because it’s just max minus min. After that, mean absolute deviation tends to feel intuitive, since it’s the average distance from the mean in the original units.

When should I use IQR instead of standard deviation?

Use IQR when your data have outliers or a skewed distribution—like income, housing prices, or wait times. IQR focuses on the middle 50% of the data and is less affected by extreme values, making it one of the best examples of a measure of variability for non-normal data.

Where can I learn more about variability and descriptive statistics?

For more formal explanations and datasets, you can explore:

• Introductory statistics materials from universities like Harvard
• Public health data and explanations from the CDC
• Research summaries and statistical methods discussions from the NIH

These sources offer real examples of how measures of variability are used in current research and policy.