Mean, Median, Mode Calculator
Calculate the mean (average), median (middle value), and mode (most frequent value) of any data set. Enter your numbers separated by commas, spaces, or new lines. Get instant results along with additional statistics like range, sum, and count.
How to Use This Mean, Median, Mode Calculator
This calculator finds all three measures of central tendency from any data set you provide. Here is how to use it effectively:
- Enter your data: Type or paste numbers into the text area. You can separate values using commas (1, 2, 3), spaces (1 2 3), line breaks (one number per line), or any combination of these formats.
- Click Calculate: Press the Calculate button to process your data and see all results instantly.
- Interpret results: The calculator displays mean, median, and mode prominently, with additional statistics (count, sum, range, min/max) shown below.
- Copy values: Click any result box to copy that specific value to your clipboard for use in other applications.
The calculator handles any size data set and works with positive numbers, negative numbers, and decimals. For mode, it correctly identifies when there is no mode (all values appear once), a single mode, or multiple modes.
What is the Mean?
The mean, commonly called the average, is the sum of all values divided by the count of values. It represents the central value of a data set when all values contribute equally. The mean is the most widely used measure of central tendency and appears in everything from grade calculations to financial analysis.
However, the mean has a significant weakness: it is sensitive to extreme values called outliers. If most students score between 70 and 90 on a test, but one student scores 20, the mean drops significantly even though most students performed well. This is why understanding all three measures of central tendency is important for accurate data interpretation.
The mean works best when data is symmetrically distributed without extreme outliers. For skewed distributions or data with outliers, the median often provides a more representative measure of the typical value.
What is the Median?
The median is the middle value when all data points are arranged in order from smallest to largest. If you have an odd number of values, the median is the single middle value. If you have an even number of values, the median is the average of the two middle values.
The median's greatest strength is its resistance to outliers. Because it only looks at position, not magnitude, extreme values do not pull the median away from the center. This makes median the preferred measure for income data, home prices, and other distributions where outliers are common.
Consider home prices in a neighborhood: if nine homes are worth $300,000 and one mansion is worth $5,000,000, the mean price is $770,000 but the median is $300,000. The median better represents what a typical home costs, while the mean is skewed by the single expensive property.
What is the Mode?
The mode is the value that appears most frequently in a data set. Unlike mean and median, mode identifies the most common value rather than a calculated center point. A data set can have:
- No mode: When all values appear exactly once, there is no mode
- One mode (unimodal): When one value appears more often than others
- Two modes (bimodal): When two values tie for most frequent
- Multiple modes (multimodal): When three or more values tie for most frequent
Mode is the only measure of central tendency that works for categorical (non-numeric) data. If surveying favorite colors, you cannot calculate a mean or median, but you can identify the mode as the most popular choice. Mode is also useful for identifying peaks in data distributions and understanding what values are most typical in a population.
Formulas and Calculations
Mean: Mean = (Sum of all values) / (Count of values)
Example: For data 2, 4, 6, 8, 10: Mean = (2+4+6+8+10) / 5 = 30 / 5 = 6
Median: Sort values and find the middle position
Example: For data 3, 7, 2, 9, 5: Sort to get 2, 3, 5, 7, 9. The median is 5 (middle value).
Example with even count: For 2, 4, 6, 8: Median = (4 + 6) / 2 = 5
Mode: Identify the most frequently occurring value(s)
Example: For 2, 3, 3, 4, 5, 3, 6: Mode = 3 (appears three times)
Range: Range = Maximum value - Minimum value
The range shows the total spread of your data from lowest to highest value.