Mean Median Mode Calculator

Compare three measures of center and see how sorting, frequencies, and outliers affect them.

Drag & drop or upload an image or PDF

Enter a data set, such as find mean, median, and mode of 7, 3, 3, 10, 12

Enter a raw list separated by commas, spaces, or line breaks. For a frequency table, write pairs such as 5:3, 6:1, 7:2.

Try an example

The center depends on the question

The mean uses every value, the median uses position after sorting, and the mode uses frequency. They can agree in a balanced data set and differ sharply when the data is skewed or contains an extreme value.

Paste the observations as a list or enter value-frequency pairs. The result keeps the sorted order and frequency counts visible, which makes the median and mode easier to check than a final answer alone.

How to use the mean median mode calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

Three measures of center

The mean is arithmetic, the median is positional, and the mode is based on repeated values. A data set may have more than one mode.

\overset{x}{ˉ} = \frac{\sum _{i = 1}^{n} x _{i}}{n}, median = middle of sorted data, mode = most frequent value

A reliable way to work through it

Count and add the values

Divide the total by the number of observations to find the arithmetic mean.

Sort before finding the median

Use the single middle value for an odd count or average the two middle values for an even count.

Build a frequency count

The most frequent value is the mode. A tie at the highest repeated frequency produces multiple modes.

Worked example

Find the mean, median, and mode of 7, 3, 3, 10, 12

3, 3, 7, 10, 12

Sort the five values from least to greatest.

\overset{x}{ˉ} = \frac{7 + 3 + 3 + 10 + 12}{5} = \frac{35}{5} = 7

Add all values and divide by the count.

median = 7

The third value is the middle of the sorted list.

mode = 3

The value 3 occurs twice, more often than any other value.

The mean is 7, the median is 7, and the mode is 3. The range is 12 minus 3, which equals 9.

Common mistakes to check

Finding the median before sorting

The median is based on ordered position, not the value that happens to appear in the middle of the input.

Choosing only one mode

If several repeated values share the highest frequency, report all of them.

Assuming mean means typical

An extreme value can pull the mean far from most observations, so the median may describe a skewed data set better.

Standard Deviation CalculatorMeasure how far values spread from the mean, with the sample or population denominator shown clearly.Z-Score CalculatorStandardize a value as a signed number of standard deviations from its mean.Probability CalculatorTranslate an event question into the right rule without assuming independence or double-counting overlap.Permutation and Combination CalculatorCount ordered arrangements and unordered selections, with the order decision made before the factorials.

Questions students ask

Can a data set have more than one mode?

Yes. If several values share the highest repeated frequency, the data is multimodal and each tied value is a mode.

What if every value appears once?

Under the common classroom convention, the data has no mode because no value occurs more often than the others.

Why can the mean and median be different?

The mean uses the size of every value, so an outlier can move it. The median depends only on ordered position and is less sensitive to extremes.

How is the median found with an even number of values?

Sort the data, identify the two middle values, and take their arithmetic mean.