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Average Calculator — Mean, Median, Mode & More

Calculate mean, median, mode, range, and standard deviation from any list of numbers. Instant statistics for students and professionals.

What is this calculator?

The average calculator computes the mean, median, mode, range, count, and sum of a list of numbers. The mean is the arithmetic average, calculated by summing all numbers and dividing by the count. It provides a quick snapshot of central tendency and spread.

Formula

Mean = (sum of all numbers) / (count of numbers). Median is the middle value when numbers are sorted; if even count, median = average of two middle numbers. Mode is the most frequent value(s). Range = maximum - minimum. Standard deviation (if included) measures dispersion.

Example

For numbers 2, 4, 4, 6, 8: sum = 24, count = 5, mean = 24/5 = 4.8. Sorted: 2,4,4,6,8, median = 4 (third value). Mode = 4 (appears twice). Range = 8-2 = 6.

How to use

  1. 1Enter your list of numbers in the input field, separated by commas or spaces. Each number can be positive, negative, or decimal.
  2. 2Click the Calculate button. The tool processes your numbers: it counts them, sums them, sorts them for median and mode, and computes range and standard deviation.
  3. 3Review the results: Mean (average), Median (middle value), Mode (most frequent), Range (spread), Count (number of entries), and Sum (total). Use these to understand your data's central tendency and variability.

Frequently Asked Questions

What is the difference between mean and median?
Mean is the arithmetic average, sensitive to outliers. Median is the middle value when data is sorted, robust to extreme values. For example, in {1,2,3,100}, mean = 26.5, median = 2.5.
How is mode calculated if no number repeats?
If no number appears more than once, the dataset has no mode. Some calculators may report 'no mode' or list all values. Our calculator returns the most frequent value(s); if all are unique, mode is undefined.
When should I use median instead of mean?
Use median for skewed distributions or when outliers are present, such as income data. Mean is appropriate for symmetric distributions without extreme values. Median better represents a typical value in skewed data.
What does the range tell me about my data?
Range = maximum - minimum. It measures the total spread of the data. A large range indicates high variability, while a small range suggests data points are close together. However, range is sensitive to outliers.
Is there a standard reference for calculating mean and median?
Yes, the formulas follow standard statistical definitions as per ISO 3534-1 and the American Statistical Association. Mean and median are fundamental descriptive statistics used universally in data analysis.
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