Mean, Median & Mode Calculator

Q: Can the mean, median, and mode all be different numbers?

Yes, and this is common in real data. For example, in the set {1, 1, 2, 3, 10}: mode = 1 (appears twice), median = 2 (middle value), and mean = 17/5 = 3.4. The large outlier (10) pulls the mean up significantly, while the repeated small value (1) anchors the mode at the lower end. This is why statisticians report multiple measures of central tendency — each tells a different story about the data's distribution.

Find the mean, median, mode, range, and sum of any data set instantly.

Data Set

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Mean (Average)

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Median—

Mode—

Range—

Sum—

Count—

How it works

Mean, median, and mode are the three measures of central tendency, and each summarizes a dataset with a single representative value in a different way. Knowing when to reach for each one is the core skill behind honest data analysis, which is why a mean median mode reading is usually reported as a group rather than in isolation. The mean (arithmetic average) adds all values and divides by the count. It's the most commonly used measure but is sensitive to outliers. A few very high or very low values can pull the mean away from where most data falls. The median is the middle value when data is sorted. It's robust to outliers and better represents 'typical' values in skewed distributions. For example, median income is often reported instead of mean income because a few billionaires can make the mean much higher than what most people earn. The mode is the most frequently occurring value — the only measure that works for categorical (non-numerical) data. A dataset can have no mode, one mode (unimodal), two modes (bimodal), or many modes (multimodal). Together with range — the spread from the minimum to the maximum — these statistics give a quick yet powerful summary of any distribution's shape and center. Analysts, teachers, economists, and researchers lean on mean median mode figures to spot skew, compare groups, and choose the single number that best describes their data before running deeper tests.

Formula

Mean = Σx / n; Median = middle value (sorted); Mode = most frequent value; Range = max − min

Each measure captures the center differently, which is why they are combined. The mean divides the total by the count, so every value pulls on the result, making it precise but outlier-sensitive. The median takes the middle of the sorted list, ignoring how extreme the ends are, so it resists outliers. The mode counts frequency, so it works even for categories. Range subtracts the smallest value from the largest to show overall spread.

Source:Introductory Statistics, OpenStax

We review all our tools from time to time to ensure accuracy.

Worked example

Data Set:3, 7, 7, 2, 9, 4

For {2, 3, 4, 7, 7, 9}: mean = 32/6 ≈ 5.33; median = (4+7)/2 = 5.5 (average of 3rd and 4th values); mode = 7 (appears twice); range = 9−2 = 7.

How to use this calculator

1
Enter your values
Enter data set.
2
Adjust the options
Fine-tune any options to match your situation.
3
Read your result
Mean (Average) updates instantly as you type — no button to press.

Frequently asked questions

When should I use mean vs median vs mode?

Use mean when data is symmetrically distributed without significant outliers — it uses all data points and is most precise. Use median when data is skewed or has outliers (like income, home prices, or ages) — it better represents the 'typical' value. Use mode for categorical data (like most popular product color) or when you want the most common value in a dataset. In many analyses, reporting all three gives the most complete picture.

What if my data set has no mode or multiple modes?

A dataset has no mode if every value appears exactly once — no value is more frequent than any other. A dataset has two modes (bimodal) if two values tie for the most frequent occurrence, and multimodal if more than two values tie. Our calculator reports all modes. Having no mode simply means there's no single most common value — this is actually common in continuous numerical data where repetition is unlikely.

How does adding an outlier affect mean vs median?

Adding an extreme outlier can dramatically shift the mean but barely affects the median. For example, in {2, 3, 4, 5, 6} the mean is 4. Adding 1000 makes it {2, 3, 4, 5, 6, 1000} with a mean of 170 — far from where most data sits. But the median only shifts from 4 to (4+5)/2 = 4.5. This resilience makes median the preferred measure when outliers are expected, such as in income or housing price distributions.

What is the relationship between mean, median, and skewness?

The relationship between mean and median reveals the shape of a distribution. If mean > median, the distribution is right-skewed (positively skewed) with a long tail toward higher values — common in income data. If mean < median, it's left-skewed (negatively skewed) with a long tail toward lower values. If mean ≈ median, the distribution is roughly symmetric. In a perfectly symmetric bell curve (normal distribution), mean, median, and mode are all equal.

Can the mean, median, and mode all be different numbers?

Yes, and this is common in real data. For example, in the set {1, 1, 2, 3, 10}: mode = 1 (appears twice), median = 2 (middle value), and mean = 17/5 = 3.4. The large outlier (10) pulls the mean up significantly, while the repeated small value (1) anchors the mode at the lower end. This is why statisticians report multiple measures of central tendency — each tells a different story about the data's distribution.