How to use the Arithmetic Mean
- Enter your values separated by commas or spaces.
- Read the mean, median, mode and count.
- Compare mean and median: a large gap indicates skew or outliers.
- Report the median instead when the gap is large.
How the calculation works
The mean is Σx ÷ n. Every observation contributes proportionally to its size, which is precisely why a single extreme value drags the mean towards it. The median — the middle value once sorted — ignores magnitude and only counts position, so it is unmoved by outliers. When mean and median coincide the distribution is roughly symmetric; when the mean sits far above the median the data is right-skewed, as incomes and house prices almost always are.
Two variants matter in practice. A weighted mean multiplies each value by its weight and divides by the sum of weights — the correct method for grades by credit hours or prices by quantity. And averaging rates requires the harmonic mean, not the arithmetic one: the average speed of a journey done at 40 and 60 is 48, not 50, because equal distances take unequal time.
Mean = Σx / n ; weighted mean = Σ(wᵢxᵢ) / ΣwᵢSource: Standard descriptive statistics definitions of mean, median and mode.
Worked example
Salaries of 28,000, 31,000, 33,000, 35,000 and 210,000.
- Sum = 337,000, n = 5.
- Mean = 337,000 / 5 = 67,400.
- Sorted middle value = 33,000, so median = 33,000.
- Four of five employees earn below the mean.
Mean 67,400 versus median 33,000 — the median is the honest summary here.
Frequently asked questions
When should I use the median instead?+
Whenever the data is skewed or contains outliers — incomes, house prices, response times.
Can a data set have no mode?+
Yes, if every value appears exactly once. It can also have several modes.
What is a weighted mean for?+
Any case where observations do not count equally, such as grades weighted by credit hours.
Why can't I average speeds arithmetically?+
Because equal distances take different times. Use the harmonic mean for rates over the same distance.
Last reviewed August 31, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.