Mean Calculator
Calculate mean instantly with our math tool. Shows detailed work, formulas used, and multiple solution methods. Free to use with no signup required.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Mean = Σx / n
Add every value in the dataset together (Σx), then divide by the number of values (n). The calculator also reports the median — the middle value once the data is sorted — for comparison, since the two measures can diverge sharply when outliers are present.
Worked Examples
Example 1: Simple average of exam scores
Problem:A student scores 78, 85, 92, 88, and 95 on five exams. Find the mean and median.
Solution:Sum = 78+85+92+88+95 = 438. Mean = 438 / 5 = 87.6. Sorted: 78, 85, 88, 92, 95 → median (middle value) = 88.
Result:Mean = 87.60, Median = 88.00
Example 2: Mean with an outlier
Problem:Five houses on a street sold for $310,000, $325,000, $298,000, $340,000, and $1,450,000 (a mansion). Find the mean and median sale price.
Solution:Sum = 2,723,000. Mean = 2,723,000 / 5 = 544,600. Sorted: 298k, 310k, 325k, 340k, 1,450k → median = 325,000.
Result:Mean = $544,600 (skewed by the mansion), Median = $325,000 (more representative)
Frequently Asked Questions
What is the arithmetic mean, and how is it different from the median?
The arithmetic mean (commonly just called 'the average') is the sum of all values divided by how many values there are. The median is the middle value when the data is sorted from smallest to largest. The mean uses every data point in the calculation, so a single extreme value (an outlier) can pull it up or down significantly, while the median ignores the actual size of extreme values and only cares about their rank — which is why median household income, for example, is usually reported instead of mean income.
How do outliers affect the mean?
Because the mean sums every value and divides by the count, one very large or very small number can shift it substantially. For example, the mean of {2, 3, 4, 5, 100} is 22.8 — far higher than any 'typical' value in the set — while the median remains 4. When a dataset has known outliers or is heavily skewed (like income or home prices), the median or a trimmed mean usually gives a more representative picture than the raw arithmetic mean.
What is the formula for the arithmetic mean?
Mean = (x₁ + x₂ + ... + xₙ) / n, often written using summation notation as x̄ = Σx / n, where Σx is the sum of all the values and n is the number of values. This is the most common of several types of 'mean' — others include the geometric mean (used for growth rates) and the harmonic mean (used for rates like speed).
When should I use the median instead of the mean?
Use the median when the data is skewed or contains outliers you don't want to dominate the result — home prices, salaries, and reaction times are classic examples. Use the mean when the data is roughly symmetric and every value should contribute proportionally, such as averaging test scores or measurement readings in a controlled experiment.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy