Average Calculator – Mean, Median, Mode & Range

How to find the mean, median and mode

The mean is what most people call the average: add every value, then divide by how many values there are. For 4, 8, 6 and 2 the sum is 20 and there are four values, so the mean is 20 ÷ 4 = 5.

The median is the middle value once the list is sorted from smallest to largest. With an odd count it is the single middle number. With an even count there are two middle numbers, and the median is halfway between them: sorted, 2, 4, 6, 8 has middle pair 4 and 6, so the median is 5.

The mode is the value that appears most often. A list can have one mode, several (if two or more values tie for most frequent, the data is bimodal or multimodal), or none at all when no value repeats. The range is the largest value minus the smallest, a quick first look at spread.

You can type or paste numbers separated by commas, spaces, semicolons or line breaks. Copying a column from a spreadsheet works as is. Negative numbers and decimals are fine. If your list uses spaces or new lines between values, a number written with a thousands comma such as 1,250 is read as one thousand two hundred fifty, and the tool tells you so. Anything that isn't a number (a stray letter, a dollar sign, a fraction like 1/2) is listed as ignored rather than silently changing your result.

Mean vs. median vs. mode: which average to use

All three describe a "typical" value, but they answer slightly different questions, and picking the wrong one is the most common way averages mislead.

• Use the mean for roughly symmetric data without extreme values: test scores in a class, daily temperatures, repeated lab measurements. It uses every value, which makes it the most informative average when the data is well behaved.
• Use the median when a few very large or very small values would drag the mean: household income, home prices, time spent waiting on hold. Half the values sit below the median and half above, no matter how extreme the ends are.
• Use the mode for categories or repeated values: the most common shoe size to stock, the most frequent answer on a 1–5 survey, the busiest hour of the day. It is the only one of the three that also works for non-numeric data.

None of the three says how spread out the data is. Two classes can both average 80, one with every score between 75 and 85 and the other ranging from 40 to 100. Read the range here, or the standard deviation for a fuller measure of spread.

Worked example: nine test scores

These are the default numbers in the calculator: 72, 85, 91, 85, 64, 98, 85, 77, 90. Sorted, they read 64, 72, 77, 85, 85, 85, 90, 91, 98.

The mean (83) sits below the median (85) because the single low score of 64 pulls the total down more than any high score pushes it up. That gap is a small sign of left skew, and it is the kind of thing you only notice when you look at more than one average.

Outliers and skewed data

An outlier is a value far from the rest. Because the mean adds everything up, one outlier can move it a long way. Take six salaries at a small firm: $42,000, $45,000, $48,000, $51,000, $55,000 and the owner's $250,000. The mean is $81,833, higher than what five of the six people earn. The median is $49,500, which describes a typical employee far better. Drop the owner and the mean falls to $48,200 while the median barely moves, to $48,000.

That pattern generalizes. In right-skewed data (a long tail of high values, like incomes or house prices) the mean sits above the median. In left-skewed data (a tail of low values, like scores on an easy test) the mean sits below it. When the mean and median are close, the data is roughly symmetric and the mean is a safe summary. This page's result note flags when the two differ noticeably.

Don't delete an outlier just because it is inconvenient. Check whether it is a typo (an extra zero) or a real value. If it is real, report the median alongside the mean, or both with and without the outlier, so readers can see its effect.

Weighted average

A weighted average lets some values count more than others. Multiply each value by its weight, add those products, then divide by the total of the weights: weighted mean = Σ(w × x) ÷ Σw.

Example: a course where homework is 20% of the grade, quizzes 30% and the final exam 50%. With a 92 homework average, 84 on quizzes and 78 on the final, the weighted average is (92 × 20 + 84 × 30 + 78 × 50) ÷ 100 = 8,260 ÷ 100 = 82.6. A simple average of the three numbers would say 84.7, overstating the grade because it treats the final as no more important than homework. To work backward from a target grade, the grade calculator shows the score you need on a final exam.

Weights don't have to add up to 100 or to 1. Credit hours, quantities bought, or the number of people in each group all work, because the formula divides by whatever they sum to. A weight of 0 simply leaves that value out. If every weight is 0 there is nothing to average, and the calculator says so instead of showing a meaningless number. Negative weights aren't accepted.

Geometric and harmonic mean

The geometric mean multiplies the values and takes the nth root. It is the right average for rates that compound, like investment returns or population growth. If something grows 10%, falls 5%, then grows 20%, the growth factors are 1.10, 0.95 and 1.20. Their geometric mean is about 1.0784, an average growth of 7.84% a year. The simple mean of 10, −5 and 20 says 8.33%, which overstates the real result. To turn a start and end value into a single growth rate, try the percentage change calculator.

The harmonic mean divides the count by the sum of reciprocals. It is the correct average for rates over the same distance or amount. Drive 60 mph to a town and 40 mph back over the same road, and your average speed is 48 mph, not 50, because you spent longer at the slower speed. Both means are only defined here when every value is above zero.

Average, median and mode in Excel and Google Sheets

Both spreadsheets use the same function names, so these formulas work in either. Assume the values are in A2:A10 and any weights in B2:B10.

The older =MODE() function still works and behaves like MODE.SNGL. If your spreadsheet result and this page disagree, the usual cause is a cell that holds a number stored as text. Spreadsheets skip those cells, but the number is still counted once you paste it here.