Mean Median Mode Range Calculator

Mean, median, mode, and range are the four foundational measures of a data set. This calculator finds all four instantly from any list of numbers — with clear explanations of what each one means.

How to Use This Calculator

1. Enter your numbers separated by commas or spaces.
2. Click Calculate to see mean, median, mode, and range — with the sorted data shown.

Definitions and Formulas

Mean (average): Sum of all values ÷ count of values.
Mean of {4, 7, 13, 16} = 40/4 = 10

Median (middle value): Sort the data; middle value for odd count, average of two middle values for even count.
Median of {4, 7, 13, 16} = (7+13)/2 = 10

Mode (most frequent): The value that appears most often. Can have multiple modes or no mode.
Mode of {4, 7, 7, 13} = 7

Range (spread): Maximum − Minimum.
Range of {4, 7, 13, 16} = 16−4 = 12

Example with a Real Dataset

Test scores: 72, 85, 85, 90, 68, 92, 85, 78

• Sorted: 68, 72, 78, 85, 85, 85, 90, 92
• Mean: 655/8 = 81.875
• Median: (85+85)/2 = 85
• Mode: 85 (appears 3 times)
• Range: 92−68 = 24

When to Use Each Measure

• Mean: Best for symmetric data without outliers. One extreme value distorts the mean significantly.
• Median: Best for skewed data or when outliers exist. Not affected by extreme values.
• Mode: Best for categorical data or when the most popular value matters (most common shoe size sold).
• Range: Quick measure of spread. Sensitive to outliers — a single extreme value makes range misleading.

Common Mistakes to Avoid

• Not sorting data before finding median — The median requires sorted data. Finding the middle value of unsorted data gives a wrong answer.
• Assuming there is always one mode — Data can be bimodal (two modes), multimodal, or have no mode if all values are different.
• Using mean to describe skewed data — Household income in the US has mean ~$105K but median ~$70K. The median better represents the typical household.

Frequently Asked Questions

Can mean and median be the same?

Yes — in a symmetric distribution, mean and median are equal. For a perfectly symmetric set like {1,2,3,4,5}: mean = 3, median = 3.

What does it mean if mode is greater than mean?

This often indicates a left-skewed (negatively skewed) distribution. Most values cluster at higher numbers, but there are some very low outliers pulling the mean down.

Is range the best measure of spread?

Not usually — range is simple but sensitive to extreme values. Standard deviation and IQR are more robust measures of spread. See our Standard Deviation Calculator.

Conclusion

Mean, median, mode, and range are the foundation of data literacy. Whether you're a student, teacher, researcher, or professional, knowing how to interpret these four measures helps you draw meaningful conclusions from any dataset.

Related: Statistics Calculator | Standard Deviation Calculator | Z-Score Calculator