Mean, Median, Mode, and Range Calculator

Find the mean, median, mode, and range of a set of numbers. Enter your data (separated by commas, spaces, or new lines) and click "Calculate" to see the full statistical breakdown and step-by-step solution.

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 data set in a different way.

Mean (Average)

The **mean** is the most common form of average. It is calculated by adding all the numbers in a set and then dividing by the count of numbers in that set.

Median (The Middle)

The **median** is the middle value in a data set that has been sorted from least to greatest. It is the number that splits the data into two equal halves.

• For an **odd** number of values, the median is the single middle number. (e.g., in 1, 3, 5, the median is 3).
• For an **even** number of values, the median is the average of the two middle numbers. (e.g., in 1, 3, 5, 7, the median is (3+5)/2 = 4).

Mode (The Most Frequent)

The **mode** is the value that appears most often in the data set. Unlike mean and median, a data set can have more than one mode, or no mode at all.

• No Mode: If all numbers appear with the same frequency (e.g., 1, 2, 3, 4).
• Unimodal: One mode (e.g., 1, 2, 2, 3, mode is 2).
• Bimodal: Two modes (e.g., 1, 1, 2, 2, 3, modes are 1 and 2).
• Multimodal: More than two modes.

Range (The Spread)

The **range** is a simple measure of the spread of the data. It is the difference between the highest value (Maximum) and the lowest value (Minimum) in the set.

Frequently Asked Questions (FAQ)

When should I use Mean, Median, or Mode?

Use the Mean for a general average when your data is not skewed (e.g., test scores).
Use the Median when your data *is* skewed by outliers (e.g., housing prices or income, where one high value would throw off the mean).
Use the Mode for categorical data (e.g., "what is the most popular color?") or to find the most common value in a set.

What if there is no mode?

If every value in a set appears only once, or if all values appear with the same frequency (e.g., 1, 1, 2, 2, 3, 3), the set has no mode. Our calculator will state "No Mode".

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Mean = (Sum of all numbers) / (Count of numbers)

Range = Maximum Value - Minimum Value