Average Calculator
Calculate the arithmetic mean, total sum, and number count.
Arithmetic, weighted, and when the plain mean lies
The arithmetic mean adds the values and divides by the count, and it is the right tool when every value carries equal weight. It stops being right the moment they do not — which is more often than people expect.
A weighted mean multiplies each value by its weight, sums, then divides by the total weight. Course grades are the everyday case: a final worth 50% and four quizzes worth 12.5% each cannot be averaged plainly. Averaging percentages computed from different-sized groups has the same problem — a 90% pass rate from 10 students and 70% from 990 is not an 80% overall rate, it is about 70.2%. For these, use the weighted average calculator.
Rates need a different mean entirely. For speeds over equal distances the correct figure is theharmonic mean: driving 60 km/h out and 30 km/h back averages 40 km/h, not 45, because you spend twice as long on the slow leg. For growth rates compounding over time the correct figure is the geometric mean. Using the arithmetic mean for either overstates the result, which is why advertised average returns often flatter reality.
Frequently Asked Questions
How is average calculated?
Add all numbers together and divide by the total count of numbers.
What is the difference between mean, median and mode?
The mean is the sum divided by the count. The median is the middle value when sorted. The mode is the most frequent value. They coincide in a symmetric distribution and diverge sharply in a skewed one - which is why median income is reported rather than mean income.
When should I use the median instead of the mean?
Whenever outliers or skew would distort the mean. In a room of ten people earning $50,000 each, one billionaire raises the mean to over $100 million while the median stays at $50,000. The median is the more honest summary of a typical value in any skewed distribution.
What is a weighted average?
An average where each value carries a weight: sum of (value x weight) divided by sum of weights. It is what you need whenever the items are not equally important - course grades weighted by credit hours, or a portfolio return weighted by position size.