Mean, Median & Mode Calculator
Calculate mean, median, mode, range, and variance for a set of numbers. Enter up to 20 values.
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How to use this calculator
Mean is the arithmetic average; median is the middle value when sorted; mode is the value that appears most often.
- 1
Enter your data values in the input fields (up to 8; optional fields are skipped if 0).
- 2
The calculator shows mean, median, mode, range, variance, and standard deviation.
- 3
Use the standard deviation calculator for larger datasets.
Frequently asked questions
When should I use mean vs median?
Use median when data is skewed or has outliers — house prices, incomes, response times. Median is resistant to extreme values. Use mean for symmetric, normally distributed data without outliers — test scores, heights, weights. The mean is influenced by every value, including extremes.
What does "no mode" mean?
A dataset has no mode when every value appears exactly once. When two or more values tie for most frequent, the dataset is bimodal or multimodal. Mode is most useful for categorical data (favourite colour, most common shoe size).
What is the difference between population and sample variance?
Population variance divides by n; sample variance divides by n−1 (Bessel's correction). Use sample variance when your data is a sample drawn from a larger population. This calculator uses population variance.
What does range tell us?
Range = maximum − minimum. It measures the total spread of data but is sensitive to outliers. A single extreme value can make range misleading. Interquartile range (IQR = Q3 − Q1) is more robust.
Measures of central tendency explained
Mean, median, and mode in context
If five employees earn $30k, $35k, $40k, $45k, and $500k: mean = $130k (misleading), median = $40k (representative), mode = no mode. Income and wealth distributions are right-skewed — always check median alongside mean when outliers are present.
Standard deviation and variance
Variance measures average squared deviation from the mean; standard deviation is the square root of variance (same units as the data). A low std dev means values cluster closely around the mean; high std dev means they are spread out. In a normal distribution, 68% of values lie within ±1 std dev of the mean.
Choosing the right measure of centre
Symmetric distribution: mean ≈ median ≈ mode; any works. Right-skewed (long tail right): mean > median > mode; use median. Left-skewed: mean < median < mode; use median. Categorical data (colours, sizes): use mode only.
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