Real-world examples of examples of skewness and kurtosis

Why start with examples of skewness and kurtosis?

Most people first meet skewness and kurtosis as formulas in a stats class. That’s unfortunate, because the best examples of these ideas come from messy, real-world data. Before we worry about equations, it helps to see how skewness and kurtosis show up in the kinds of distributions you already know: income, test scores, wait times, and more.

Think of it this way:

• Skewness tells you which side of the distribution has the long tail.
• Kurtosis tells you how heavy those tails are and how sharp or flat the peak is compared to a normal distribution.

With that in mind, let’s walk through concrete examples of examples of skewness and kurtosis, one domain at a time, and translate the jargon into something you can actually recognize in a chart or a spreadsheet.

Classic right-skewed distributions: Income and wealth

If you want a textbook example of positive skewness, look at income or wealth data.

In almost every country, most people earn moderate incomes, while a relatively small number earn extremely high incomes. That creates a right-skewed distribution:

• A big cluster of values on the left (low to middle incomes)
• A long tail stretching to the right (very high incomes)

This is one of the cleanest real examples of skewness:

• Mean > Median > Mode — the average income gets pulled to the right by high earners.
• Skewness > 0 — positive skew.
• Kurtosis often > 3 (leptokurtic) — because of a few very large outliers.

In the U.S., income data from the Census Bureau and IRS routinely show this pattern. A small fraction of households holds a large share of total wealth, which leads to heavy right tails. That’s exactly the kind of pattern kurtosis is meant to capture: there’s more probability mass in the tails than you’d expect under a normal distribution.

So in income data, you get a two-for-one: a clear example of skewness and a clear example of high kurtosis at the same time.

Left-skewed distributions: Retirement age and exam scores

Right-skewed examples get all the attention, but left-skewed (negatively skewed) distributions matter just as much.

Retirement age

In many developed countries, most people retire within a fairly narrow age band (say, 60–70), but there are more people who retire earlier than average than people who retire much later. That creates a left tail:

• A cluster around the normal retirement age
• A tail stretching to the left (people who retire very early)

This gives you:

• Mean < Median — the early retirements pull the average down.
• Skewness < 0 — negative skew.

The shape isn’t always as dramatic as income, but it’s a practical example of skewness in labor statistics.

High-scoring exams

Another accessible example of examples of skewness and kurtosis comes from exams that are too easy for the test-takers.

Imagine a certification exam where most candidates are well-prepared:

• Many scores are bunched near the top (80–100%)
• Few people score very low

The distribution becomes left-skewed:

• A heap of scores near the maximum
• A tail extending to the left (lower scores)

Depending on how extreme the clustering is, kurtosis can also be high, because you might see a sharp pile-up near the top score and relatively thin tails elsewhere.

Testing agencies and education researchers often have to correct for this, using item-response theory or scaling methods so the score distribution behaves more like a normal curve. But before any of that modeling, they’re staring at a simple example of skewness and kurtosis.

Hospital wait times: Skewness in health care operations

If you’ve ever sat in an emergency department and felt like you were waiting forever, you’ve experienced another real example of skewness.

Hospital and emergency department wait times typically show:

• Many patients seen in a moderate time window
• A smaller number who wait much longer due to crowding, triage priorities, or resource shortages

That leads to a right-skewed distribution of wait times:

• Most values clustered at lower to moderate wait times
• A long right tail of very long waits

From an analytics perspective:

• Skewness > 0 — positive skew.
• Kurtosis often elevated — those very long waits act like outliers and add weight to the right tail.

Health services researchers and agencies like the Centers for Disease Control and Prevention (CDC) and National Institutes of Health (NIH) routinely analyze these distributions to improve operations and patient safety. You can see related health statistics and methodology discussions at:

• https://www.cdc.gov
• https://www.nih.gov

Here, examples of examples of skewness and kurtosis aren’t just academic. They inform staffing models, triage policies, and quality-of-care benchmarks.

Stock returns: Fat tails and high kurtosis in finance

Financial data give some of the best examples of kurtosis, especially when markets get volatile.

Daily stock returns for major indices (like the S&P 500) might look roughly symmetric over long periods, so skewness can hover near zero. But when analysts compute kurtosis, they often find:

• Kurtosis > 3 (leptokurtic) — meaning fat tails compared to a normal distribution.

Translated:

• Extreme gains and losses happen more often than a normal model would predict.
• The distribution has more mass in the tails and a sharper central peak.

This is not a small technical detail. Risk models that assume normal returns tend to underestimate the probability of large crashes or rallies. That’s why modern risk management and stress testing explicitly examine kurtosis and tail risk.

So even when skewness is mild, kurtosis becomes the star. Financial data are a textbook example of examples of skewness and kurtosis where kurtosis does most of the heavy lifting in explaining risk.

Environmental data: Air pollution and extreme events

Environmental datasets, especially those involving extreme events, are packed with informative examples of skewness and kurtosis.

Take daily measurements of a pollutant like PM2.5 (fine particulate matter) in a major city:

• Most days fall in a low to moderate range.
• Occasionally, wildfires, industrial incidents, or weather patterns cause spikes in pollution.

The result:

• Right-skewed distribution — most days are relatively clean, but a few days are extremely polluted.
• High kurtosis — those spikes are outliers that thicken the right tail.

Agencies like the Environmental Protection Agency (EPA) and public health researchers use these distributions to:

• Set air quality standards
• Issue health advisories
• Model long-term exposure risk

While the EPA is a .gov authority, you can also find health-focused discussions of pollutant effects on sites like Mayo Clinic (https://www.mayoclinic.org) and CDC (https://www.cdc.gov). Behind many of those risk analyses are real examples of skewness and kurtosis.

Tech and online behavior: Clicks, views, and engagement

Modern tech platforms generate some of the clearest digital-era examples of examples of skewness and kurtosis.

Consider video views on a large platform:

• Most videos get modest view counts.
• A small fraction go viral and attract millions of views.

The distribution of views per video is:

• Heavily right-skewed — long tail of very high counts.
• High kurtosis — viral hits are massive outliers.

The same pattern shows up in:

• Likes or favorites per post
• Shares or retweets
• App usage time per user

Data scientists at these companies pay close attention to skewness and kurtosis when:

• Designing recommendation algorithms
• Detecting anomalies (e.g., fake traffic)
• Choosing transformations (like log scales) before modeling

If you’ve ever plotted log-transformed views or income data and suddenly everything “looks normal,” you’ve just tamed an extreme example of skewness and kurtosis.

When skewness and kurtosis mislead: The problem of outliers

Not every example of skewness and kurtosis is helpful. Sometimes, these measures are dominated by a handful of outliers.

Imagine a small dataset of monthly sales for a startup:

• Eleven months show sales between \(10,000 and \)20,000.
• One month has a huge $250,000 contract.

On paper, you get:

• Strong positive skewness — that one big month stretches the right tail.
• Very high kurtosis — extremely heavy tail.

But from a practical standpoint, you might say, “This is just one weird month, not the real shape of our business.” This is a reminder that:

• Skewness and kurtosis are sensitive to outliers.
• They should be interpreted alongside plots (histograms, boxplots, density curves) and context.

Real examples of skewness and kurtosis are most informative when they reflect a consistent pattern, not a single data glitch or one-off event.

How analysts use examples of skewness and kurtosis in 2024–2025

In current analytics practice, examples of examples of skewness and kurtosis show up in several recurring workflows.

Model choice and transformation

Before fitting models, analysts often:

• Check skewness to decide whether to use a log, square-root, or Box–Cox transformation.
• Inspect kurtosis to gauge tail behavior and whether normal-based methods are appropriate.

For instance:

• Right-skewed income or sales → log transformation to stabilize variance and reduce skew.
• High-kurtosis financial returns → heavy-tailed models (e.g., t-distributions) instead of simple normal models.

Risk and reliability analysis

In finance, insurance, and engineering:

• High kurtosis signals higher-than-expected extreme events.
• Skewness indicates whether the risk is more on the loss side or the gain side.

Think of:

• Insurance claims with rare but massive payouts (right-skewed, high kurtosis)
• Component lifetimes where early failures are more common than late catastrophic failures (left-skewed patterns in some reliability contexts)

Policy and public health decisions

Public health agencies and researchers use real examples of skewness and kurtosis when they:

• Analyze disease incidence (rare but severe outbreaks create skewness and heavy tails)
• Study hospital utilization and length of stay (often right-skewed with high kurtosis)

Work from institutions like Harvard T.H. Chan School of Public Health (https://www.hsph.harvard.edu) and NIH often involves distributions that are far from normal, where skewness and kurtosis indicate how far reality is from the textbook bell curve.

Quick mental “templates” for common shapes

To make these ideas stick, it helps to have a mental library of best examples you can recall quickly:

• Right-skewed, high kurtosis
  Income, wealth, online views, hospital wait times, pollution spikes, insurance claims.

• Right-skewed, moderate kurtosis
  Daily step counts, time spent on a hobby app, small-business monthly revenue.

• Left-skewed, moderate kurtosis
  Easy exam scores, some retirement age distributions, grades in a class with grade inflation.

• Near-symmetric, high kurtosis
  Financial returns with frequent moderate moves and occasional crashes or rallies.

Whenever you’re handed a dataset, ask yourself: Which of these examples of skewness and kurtosis does this feel like? That quick comparison can guide your expectations before you even compute the numbers.

FAQ: Common questions about examples of skewness and kurtosis

What is a simple real-life example of skewness?

A very simple real-life example of skewness is household income in a country. Most households earn around the middle of the income range, but a small number earn very high incomes. That creates a right-skewed distribution where the mean is higher than the median and there is a long tail of high-income values.

What is a simple real-life example of kurtosis?

A clean example of kurtosis is daily stock market returns. Over time, returns look roughly centered around zero, but you see more extreme positive and negative days than a normal distribution would predict. That pattern — more probability in the tails and a sharper peak in the middle — is a sign of high kurtosis.

Can a distribution have skewness without high kurtosis?

Yes. A distribution can be clearly skewed but have kurtosis close to that of a normal distribution. For instance, a moderately right-skewed distribution of daily step counts might show a long right tail (people who walk a lot more) but not many extreme outliers. Skewness picks up the asymmetry, while kurtosis stays closer to normal.

Can a distribution have high kurtosis but almost no skewness?

Also yes. Financial returns are a common example of examples of skewness and kurtosis where kurtosis is high but skewness is near zero. The distribution is roughly symmetric around zero, but extreme gains and losses happen more often than a normal model predicts, which inflates kurtosis.

Why do analysts care about examples of examples of skewness and kurtosis?

Analysts care because these measures warn you when normal-model assumptions are shaky. Real examples of skewness and kurtosis tell you whether:

• A transformation might be helpful
• Heavy-tailed models are more appropriate
• Standard confidence intervals and hypothesis tests might misrepresent risk or uncertainty

In other words, examples of skewness and kurtosis help bridge the gap between neat theory and messy real-world data.