Mean, Median, Mode Calculator

Enter a set of numbers to compute descriptive statistics and visualize data with a box-and-whisker plot

By Drew Budwin · Last updated July 2026 · Methodology

Separate numbers with commas, spaces, or new lines. Up to 1,000 values.

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How We Calculate This

Picking the Right Average for the Data

Mean works best when data is symmetric with no outliers. Median is better for skewed data. One billionaire doesn't move the median household income the way it moves the mean. Mode matters for categorical data: the most common shoe size to stock isn't the average shoe size.

Worked Example: 2, 3, 3, 7, 10

Mean = 25 ÷ 5 = 5. Median = 3 (the 3rd value when sorted). Mode = 3 (appears twice). Add an outlier of 100 and the mean jumps to roughly 20.8, but the median moves only to (3 + 7) ÷ 2 = 5. Same data, very different story depending on which average you report.

Mean, Median, Mode Calculator Formula

The arithmetic mean is the sum of all values divided by the count:

mean = (x₁ + x₂ + … + xₙ) / n

where x₁ through xₙ are the data values and n is the count.

Quartiles use Tukey's hinges method. The IQR measures the spread of the middle 50% of the data:

IQR = Q3 − Q1

where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile).

Outliers are identified using the 1.5 × IQR rule:

outlier if x < Q1 − 1.5·IQR or x > Q3 + 1.5·IQR

Values strictly outside these fences are flagged as outliers and shown as dots beyond the whiskers in the box plot.

How to Use This Calculator

  1. Enter your numbers in the Dataset field. Separate values with commas, spaces, or new lines. You can mix delimiters freely.
  2. You may enter up to 1,000 numbers. Negative numbers and decimals are fully supported.
  3. Click Calculate to compute all descriptive statistics.
  4. Review the results: count, sum, mean, median, mode, range, min, max, Q1, Q2, Q3, IQR, and outliers.
  5. Examine the box-and-whisker plot below the statistics cards. It shows the five-number summary and marks any outliers as individual dots.
  6. Share your results by copying the URL. The dataset is encoded in the link so anyone can reproduce the calculation.

Frequently Asked Questions

What is the difference between mean and median?

The mean is the arithmetic average: sum divided by count. The median is the middle value when data is sorted. When a dataset has extreme outliers (like a few very large values), the median is often a better measure of the 'typical' value because it is not pulled by the extremes the way the mean is. To express differences between values as percentages, try the percentage calculator.

What does 'No mode' mean?

A dataset has no mode when every value appears the same number of times (uniform distribution). For example, [1, 2, 3, 4] has no mode because each number appears exactly once. If two values tie for the highest frequency, both are reported as modes (bimodal distribution).

How are quartiles calculated?

This calculator uses Tukey's hinges (the inclusive method). The dataset is sorted and split into a lower half and an upper half at the median. Q1 is the median of the lower half and Q3 is the median of the upper half. When the dataset has an odd count, the median itself is excluded from both halves. This is the most common method in introductory statistics courses.

What is the IQR and why does it matter?

The interquartile range (IQR) is Q3 − Q1 and represents the spread of the middle 50% of the data. It is a robust measure of spread that is not affected by extreme outliers, unlike the range (max − min). A small IQR means the middle of the dataset is tightly clustered; a large IQR means it is spread out.

How does the outlier detection work?

This calculator uses the standard 1.5 × IQR rule. A value is flagged as an outlier if it falls strictly below Q1 − 1.5 × IQR (the lower fence) or strictly above Q3 + 1.5 × IQR (the upper fence). Outliers appear as individual dots beyond the whiskers in the box plot.

What is standard deviation?

Standard deviation measures how spread out the values are from the mean. A low standard deviation means values cluster tightly around the mean, while a high standard deviation indicates they are spread over a wider range. This calculator shows both population and sample standard deviation.

How do I read the box-and-whisker plot?

The box spans Q1 to Q3, so its width shows the IQR. The line inside the box is the median. The whiskers extend to the smallest and largest non-outlier values within 1.5 × IQR of the box edges. Dots beyond the whiskers are outliers. A box shifted far to one side of center signals a skewed distribution.

What does it mean when my data is bimodal or multimodal?

Bimodal means two values tie for highest frequency; multimodal means three or more do. This often signals that your dataset contains two distinct groups. For example, heights of adults in a mixed-sex sample tend to cluster around two peaks. A single mean or median can be misleading for such data; consider analyzing each group separately.

When does the IQR matter more than the range?

The range (max minus min) is dominated by the most extreme values in your data, so a single outlier can make it look wide. The IQR covers only the middle 50%, making it a better measure of typical spread when outliers are present. If your min and max are far from everything else, trust the IQR.

Population vs. sample standard deviation: which should I use?

Use population standard deviation when your dataset is the complete group you care about (all exam scores for one class). Use sample standard deviation when your data is a subset of a larger population and you're estimating that population's spread (a survey sample). Sample standard deviation divides by n − 1 instead of n to correct for the underestimate that comes from working with a sample.

Further Reading

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