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 for accuracy by Manoj Kumar, Mathematics Educator
Mean Calculator
Calculator
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Formula: Mean = Σx / n
Worked example — Mean = 87.60, Median = 88.00
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.
How do I calculate the mean of a large dataset by hand versus with a calculator?
By hand, you add every value together and divide by the count — manageable for a handful of numbers but error-prone and slow for dozens or hundreds of entries. Mean Calculator removes that risk: paste any comma-separated list of numbers and it instantly returns both the mean and median, so you can cross-check a hand calculation or process a large dataset in seconds.
Does the order of the numbers I enter change the mean?
No. Addition is commutative, so the sum — and therefore the mean — is identical no matter what order the numbers are entered in. The median, however, requires the values to be sorted internally before the middle value is identified; the calculator handles that sorting automatically.
What is a weighted mean, and how does it differ from a simple mean?
A simple (arithmetic) mean treats every value equally. A weighted mean multiplies each value by a weight reflecting its relative importance before averaging — for example, a course grade where the final exam counts twice as much as a quiz. Mean Calculator computes the simple, equally-weighted mean; if your values need different weights, multiply the more important ones by their weight and adjust the divisor accordingly, or use a dedicated weighted-average tool.
Where is the arithmetic mean used in real life?
Averages appear constantly in daily life and professional work: a teacher averaging quiz scores to assign a grade, a runner averaging their mile splits, a business averaging monthly revenue to forecast next quarter, a meteorologist averaging decades of temperature readings to establish a climate baseline, and a nutritionist averaging daily calorie intake across a week to check against a target.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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