Mean Median Mode Calculator

Enter a dataset to get mean, median, mode, range, and standard deviation instantly.

📖 What are Mean, Median, and Mode?

Mean, median, and mode are the three primary measures of central tendency in statistics. They each describe the "center" of a dataset in a slightly different way, and understanding all three gives a much more complete picture of your data than any single measure alone.

Mean (arithmetic average) is calculated by summing all values and dividing by the count. It is the most commonly used measure and works best for symmetrically distributed data without extreme outliers.

Median is the middle value when data is sorted in ascending order. For an even number of data points, it's the average of the two middle values. The median is unaffected by extreme outliers, making it ideal for skewed distributions like income, house prices, or response times.

Mode is the value that appears most frequently. A dataset can have zero modes (all values unique), one mode (unimodal), or multiple modes (bimodal, trimodal, etc.). Mode is the only measure of central tendency that can be used with categorical data.

Along with these three measures, this calculator also computes range (the spread from minimum to maximum), variance (average squared deviation from the mean), and standard deviation (square root of variance - the most commonly used measure of spread).

📐 Formula

Mean = Sum of all values / Count

Median = Middle value (sorted data)

Mode = Most frequently occurring value(s)

Range = Maximum − Minimum

Variance (sample) = Σ(xᵢ − mean)² / (n − 1)

Std Dev = √Variance

📖 How to Use This Calculator

Enter your numbers in the text box, separated by commas or spaces.

Click Calculate.

Mean, median, mode, range, standard deviation, and variance are shown instantly along with the sorted dataset.

💡 Example Calculations

Example 1 - Test scores

Scores: 72, 85, 90, 72, 88, 64, 91, 72, 78, 80

Sorted: 64, 72, 72, 72, 78, 80, 85, 88, 90, 91

Sum = 792, Count = 10

Mean = 792 / 10 = 79.2

Median = (78 + 80) / 2 = 79

Mode = 72 (appears 3 times)

Range = 91 − 64 = 27

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Example 2 - Skewed data with an outlier

Salaries (₹ lakhs): 5, 6, 5.5, 6, 5.8, 6.2, 40

Mean = 74.5 / 7 = 10.64 lakhs (skewed by the ₹40 lakh outlier)

Median = 6 lakhs (more representative)

Mode = 5 and 6 lakhs (bimodal)

This shows why median is preferred for income data - the mean is misleadingly high.

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Frequently Asked Questions

What is the difference between mean, median, and mode?+

Mean is the arithmetic average (sum divided by count). Median is the middle value when data is sorted. Mode is the most frequently occurring value. For symmetric distributions, all three are equal. For skewed data, they differ - which is why understanding all three gives a complete picture.

When should I use median instead of mean?+

Use median when your data contains outliers or is skewed. For example, average household income uses median because a few billionaires would make the mean misleadingly high. Median house prices, median salaries, and median response times are also better represented by the median.

Can there be no mode in a dataset?+

Yes - if every value in the dataset appears exactly once, there is no mode. Some datasets have multiple modes (bimodal or multimodal) when two or more values appear equally often and more frequently than others.

What does range tell us about data?+

Range = Maximum - Minimum. It measures the total spread of data. A large range indicates high variability; a small range indicates consistency. However, range is sensitive to extreme values - a single outlier can make the range appear very large.

How is standard deviation different from range?+

Range only uses two data points (min and max). Standard deviation uses all data points and measures how far values typically deviate from the mean. Standard deviation is a more robust and informative measure of spread.

What does the range tell you about a dataset?+

The range is the simplest measure of spread (dispersion). It equals the maximum value minus the minimum value. Example: for {4, 7, 13, 2, 9}: range = 13 - 2 = 11. The range is easy to calculate but sensitive to outliers - a single extreme value makes the range large even if most values are clustered close together. For a more robust measure of spread, use interquartile range (IQR) or standard deviation.

Why is variance squared instead of just using the average deviation?+

Variance uses squared differences (from the mean) rather than absolute differences for two reasons: (1) Squaring makes all differences positive without using absolute value, which allows calculus-based optimisation. (2) Squared distances have important mathematical properties in statistics and are linked to the least squares principle used in regression. The downside is that variance is in squared units. Taking the square root gives standard deviation, which is back in the original units and more interpretable.

How do I find the median of an even number of values?+

When a dataset has an even number of values, there is no single middle value. Sort the data, then take the average of the two middle values. Example: {3, 7, 12, 19} has 4 values. The two middle values are 7 and 12. Median = (7 + 12) / 2 = 9.5. This is the standard definition used in statistics, ensuring the median always divides the data so that half the values are below and half are above.