Mean, Median, Mode, Range Calculator

What this calculator does

This calculator summarizes a data set with the four most common descriptive measures: mean, median, mode, and range. It also reports the count, sum, smallest value, largest value, geometric mean, and the sorted version of the data. Together these numbers describe both the center and the spread of a list without requiring any statistical software.

Each measure answers a slightly different question. The mean gives the arithmetic average. The median identifies the middle observation after sorting. The mode reports the most frequent value. The range shows the distance between the minimum and the maximum. Looking at all four together often reveals whether a data set is symmetric, skewed, or contains repeated values.

How to use this calculator

1. Enter the numbers separated by commas, spaces, semicolons, or new lines.
2. Click Calculate.
3. Read the headline mean and the summary rows for the median, mode, range, count, sum, and sorted data.

The order of the input does not matter. The calculator sorts the data internally before finding the median and displays the sorted list so you can verify the middle position yourself.

Formulas

Mean = (Σ x_i) / N

Median = middle value of the sorted data
         (average of the two middle values when N is even)

Mode = value or values with the highest frequency

Range = maximum − minimum

Geometric mean = (x_1 × x_2 × ... × x_N)^(1/N)

The geometric mean is calculated only when every value is positive, because a zero or negative value makes the product-based formula undefined in this context.

Default example

The default data set is 10, 2, 38, 23, 38, 23, 21. Sorted, it becomes 2, 10, 21, 23, 23, 38, 38. The sum is 155 and the count is 7, so the mean is about 22.142857. The median is 23, the middle value of the sorted list.

Both 23 and 38 appear twice, so the data set is bimodal and the calculator reports both values. The range is 38 − 2 = 36, the smallest value is 2, and the largest is 38. The geometric mean of the positive values is about 16.412764.

Assumptions and limitations

• The input must contain at least one number. The calculator does not treat blank entries as zero.
• The mean uses every observation and is sensitive to outliers. The median is usually a better summary when the data is heavily skewed.
• A data set can have no mode when every value appears exactly once. It can also have several modes when multiple values tie for the highest frequency.
• The range uses only two observations, so it ignores everything between the minimum and the maximum. It is a quick measure of spread, not a complete one.
• The calculator does not weight values. If some observations represent many underlying cases, use a weighted mean instead.
• Floating-point rounding may affect the last displayed digits for very long decimal inputs.

Frequently asked questions

Should I report the mean or the median?

Report the median when the data contains outliers or is strongly skewed, such as income or house prices. Report the mean when the values are roughly symmetric and every observation should carry equal weight. Showing both is often the clearest choice because the gap between them reveals skew.

What does it mean when there is no mode?

No mode means that every value in the data set appears the same number of times. When all values are unique, no value is more frequent than the others, so the calculator reports "No mode" instead of choosing an arbitrary value.

Can a data set have more than one mode?

Yes. A data set is bimodal when two values tie for the highest frequency, and multimodal when three or more values tie. The calculator lists every value that shares the maximum frequency.

Source

Reference: Calculator.net — Mean, Median, Mode, Range Calculator.