# Mean, Median & Mode Calculator

Calculate mean, median, and mode of any data set instantly. Also shows count, sum, and range. Free online central tendency calculator for students.

## What this calculates

Find the mean, median, and mode of any data set with this free calculator. Simply enter your numbers separated by commas, and instantly get all three measures of central tendency along with the count, sum, and range of your data.

## Inputs

- **Data Set** — Enter numbers separated by commas. Example: 12, 15, 18, 22, 15, 30

## Outputs

- **Mean (Average)** — The sum of all values divided by the count of values.
- **Median** — The middle value when data is sorted in order.
- **Mode** — formatted as text — The value(s) that appear most frequently.
- **Count** — The number of values in the data set.
- **Sum** — The total sum of all values.
- **Range** — The difference between the largest and smallest values.

## Details

Mean, median, and mode are the three primary measures of central tendency in statistics. Each provides a different perspective on what is 'typical' in a data set.

Mean (Arithmetic Average)

The mean is calculated by adding all values and dividing by the number of values. Formula: Mean = Sum / Count. The mean is sensitive to outliers -- a single very large or small value can significantly shift the mean.

Example: For the data set {3, 7, 7, 19, 24}, Mean = (3 + 7 + 7 + 19 + 24) / 5 = 60 / 5 = 12.

Median

The median is the middle value when data is arranged in order. For an odd number of values, it is the exact middle value. For an even number, it is the average of the two middle values. The median is resistant to outliers.

Example: For {3, 7, 7, 19, 24}, the median is 7 (the 3rd value in a sorted list of 5).

Mode

The mode is the value that appears most frequently. A data set can have one mode (unimodal), multiple modes (multimodal), or no mode (if all values appear with equal frequency).

Example: For {3, 7, 7, 19, 24}, the mode is 7 (appears twice).

When to Use Each

- Mean: Best for symmetric distributions without outliers

- Median: Best when data has outliers or is skewed

- Mode: Best for categorical data or identifying the most common value

## Frequently Asked Questions

**Q: What is the difference between mean, median, and mode?**

A: The mean is the arithmetic average (sum divided by count). The median is the middle value when data is sorted. The mode is the most frequently occurring value. For a perfectly symmetric distribution, all three are equal. For skewed data, they differ and each tells you something different about the data.

**Q: When should I use the median instead of the mean?**

A: Use the median when your data has outliers or is heavily skewed. For example, when analyzing household incomes, a few very high earners can inflate the mean, making the median a better representation of a 'typical' income. The median is also preferred for ordinal data.

**Q: Can a data set have more than one mode?**

A: Yes. A data set with two modes is called bimodal, and one with more than two is called multimodal. For example, in the set {1, 2, 2, 3, 3, 4}, both 2 and 3 are modes because each appears twice. If every value appears only once, there is no mode.

**Q: How do I find the median of an even number of values?**

A: When the data set has an even number of values, the median is the average of the two middle values. For example, for {2, 5, 8, 12}, the two middle values are 5 and 8, so the median is (5 + 8) / 2 = 6.5.

**Q: What is the range and how is it different from these measures?**

A: The range is the difference between the largest and smallest values in a data set. Unlike mean, median, and mode (which measure central tendency), the range measures spread or variability. For {3, 7, 7, 19, 24}, the range is 24 - 3 = 21.

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Source: https://vastcalc.com/calculators/statistics/mean-median-mode
Category: Statistics
Last updated: 2026-04-21