Calculate mean, median, mode, range, variance and standard deviation from any list of numbers, plus weighted averages for grades and portfolios.
Paste from Excel or type manually. Negative numbers and decimals supported.
Weighted mean = sum(value x weight) / sum(weights). Typical use: grades by credits, portfolio returns.
Mean (arithmetic average)
Enter numbers to calculate
Show sorted values
Statistic reference
Statistic
Formula
When to use
Mean
sum / n
Symmetric data, no outliers
Median
middle sorted value
Skewed data, income, house prices
Mode
most frequent value
Categorical, discrete data
Geometric mean
(x1 x x2 ... xn)^(1/n)
Growth rates, ratios (positive only)
Harmonic mean
n / sum(1/xi)
Averages of rates (speed, density)
Range
max - min
Quick spread measure
Variance
sum((xi - mean)^2) / n
Spread around mean
Std deviation
sqrt(variance)
Same units as data; normal distribution
Frequently asked questions
Mean is the arithmetic average (sum divided by count). Median is the middle value when data is sorted. Mode is the value that appears most often. For symmetric data all three are close. For skewed data (like incomes) the median gives a better sense of "typical" than the mean, which is pulled by outliers.
Use the median whenever your data has outliers or a skewed distribution. Examples: home prices, salaries, reaction times. One billionaire in a room makes the mean income misleading while the median stays realistic. The mean works best for symmetric distributions such as heights or measurement errors.
Population standard deviation divides by n and is used when your data represents the entire group. Sample standard deviation divides by n-1 and is used when your numbers are a sample drawn from a larger population; the n-1 correction (Bessel's correction) compensates for the fact that a sample tends to underestimate variability. In most practical cases (surveys, experiments) use the sample version.
Standard deviation measures how spread out your numbers are around the mean, in the same units as the data. A small std deviation means values cluster near the mean; a large one means they are scattered widely. For normally distributed data, about 68% of values lie within one standard deviation of the mean and about 95% within two.
A weighted average multiplies each value by its weight, sums the products, then divides by the sum of the weights: (v1*w1 + v2*w2 + ... + vn*wn) / (w1 + w2 + ... + wn). Use it when some items matter more than others, for example a GPA where each course grade is weighted by its credit hours, or a price index weighted by quantity.
Use the geometric mean for multiplicative data like growth rates, interest rates or percentage changes - it avoids overstating the average that the arithmetic mean would give. Use the harmonic mean for averaging rates with a common numerator, for example average speed over fixed distances. Both work only with positive numbers.
The Average Calculator computes a full set of descriptive statistics from any list of numbers you paste or type in. Enter values separated by spaces, commas, semicolons or new lines and the calculator instantly returns the arithmetic mean, median, mode, minimum, maximum, range, sum, count, geometric mean, harmonic mean, variance and standard deviation (population and sample versions).
A weighted average mode is built in for cases where each value carries a different weight, such as course grades weighted by credits or portfolio returns weighted by position size. You can also view the full sorted list of values to spot outliers, and copy any statistic to the clipboard with one click.
Example: for the numbers 12, 17, 23, 8, 45, 32, 9, 21, 14, 28 the calculator reports mean 20.9, median 19, range 37 and sample standard deviation about 11.7. A reference table explains when to use each measure and the FAQ covers common questions about mean vs median, population vs sample standard deviation, and how weighted averages work.