Average
calculator.
Paste or type a list of numbers to get the mean, median and mode together with the range, sum, count and both standard deviations, so you can tell whether the average describes your data well.
Three averages,
one story.
- Mean = sum ÷ count.
- Median = the middle value when sorted (the average of the two middle values for an even count).
- Mode = the most frequent value; there may be several or none.
- Standard deviation: population divides by n, sample divides by n − 1.
How do you calculate the average of a list of numbers?
Add the numbers and divide by how many there are. For 72, 85, 85, 90, 64, 78 and 95 the sum is 569 and the count is 7, so the mean is about 81.29. The median, the middle value once sorted, is 85.
Mean or median?
The mean uses every value, so a single extreme value pulls it. Five house prices of 250, 270, 280, 300 and 1,500 thousand have a mean of 520 thousand but a median of 280 thousand. When the mean and median differ a lot, the median is usually the better description of a typical value; the calculator warns you when that happens.
Sample or population standard deviation?
Standard deviation measures how spread out the values are. If your numbers are the whole group you care about, divide by n (population). If they are a sample used to estimate a larger group, divide by n − 1 (sample), which corrects for the sample’s tendency to understate spread. For 2, 4, 4, 4, 5, 5, 7, 9 the population figure is 2 and the sample figure is about 2.14.
Typing numbers
Separate values with spaces, line breaks, semicolons or commas. Decimal commas such as 1,5 work when values are separated by spaces, and thousands separators such as 1,000 are understood.
Worked examples.
Test scores
Seven test scores: 72, 85, 85, 90, 64, 78, 95.
Mean ≈ 81.29 (569 ÷ 7), median 85, mode 85, range 31.
Load this exampleAn outlier pulls the mean
Five house prices in thousands: 250, 270, 280, 300, 1,500.
Mean 520 but median 280: the median is the better typical price.
Load this exampleSample standard deviation
Measurements 2, 4, 4, 4, 5, 5, 7, 9.
Mean 5; population standard deviation 2; sample standard deviation 2.1380899353.
Load this exampleDecimal commas
Values typed European-style: 1,5 2,5 3,5.
Mean 2.5.
Load this exampleWhat this calculator
does not do.
- Up to 10,000 values.
- It does not calculate weighted averages, quartiles or confidence intervals.
- Values are treated as plain numbers; units are not checked.
Common questions.
What is the difference between mean and average?
In everyday use “average” usually means the arithmetic mean. Statisticians also call the median and mode averages, because each describes a typical value.
Can a data set have no mode?
Yes. If no value appears more than once there is no mode, and if several values tie for most frequent there are several modes.
What is the geometric mean?
The nth root of the product of n positive numbers. It suits growth rates and ratios; the calculator shows it when every value is positive.
- NIST/SEMATECH e-Handbook of Statistical Methods, Measures of Location — mean, median and mode
- NIST/SEMATECH e-Handbook, Measures of Scale — variance and standard deviation with N − 1
Compensated (Neumaier) summation; tests include textbook data sets, list-parsing cases and 200 randomized lists checked against a naive two-pass implementation.