Average Calculator

The mean is the most common type of average. Add all numbers together and divide by the count.

Our calculator shows each step of the calculation and handles any number of values.

Calculate weighted averages when values have different importance.

Perfect for:

• grade calculations
• portfolio returns
• any situation where some values count more than others

Find the middle value of your data set.

The median is less affected by outliers than the mean, making it useful for skewed distributions like income or house prices.

Identify the most frequently occurring value(s) in your data.

A data set can have:

• no mode
• one mode (unimodal)
• multiple modes (bimodal/multimodal)

Calculate your average grade or GPA.

Enter your scores and optional weights for different assignments or courses to get your overall average.

Get comprehensive statistics including:

• sum
• count
• minimum
• maximum
• range
• variance
• standard deviation

Perfect for data analysis and statistical research.

An average is a single number that summarizes a set of values by representing their central tendency. The most familiar average is the arithmetic mean, found by adding every value and dividing by how many there are.

According to Encyclopaedia Britannica, the term "mean" broadly covers several measures of the center of a distribution, including the arithmetic, geometric, and harmonic means.

Averages work because they collapse many observations into one representative figure you can compare across groups. For example, the mean of 4, 8, and 12 is (4 + 8 + 12) / 3 = 8.

Khan Academy notes that mean, median, and mode each capture the center differently, so the best choice depends on your data.

To calculate the arithmetic mean, use the formula Mean = (x₁ + x₂ + ... + xₙ) / n, where n is the count of values. First add every number to get the sum, then divide by how many values you have.

Wolfram MathWorld defines this arithmetic mean as the sum of the sample values divided by the sample size.

Worked example: for 10, 20, 30, 40, 50 the sum is 150 and the count is 5, so the mean is 150 / 5 = 30. The method never changes with more numbers, only the sum and count grow.

Enter your values above and the calculator shows each arithmetic step automatically.

The geometric mean multiplies all n values and takes the nth root — equivalently, it is the antilog of the mean of their logarithms, a relationship you can verify with a logarithm calculator — making it ideal for growth rates, ratios, and compounding returns; the geometric mean of 4 and 9 is √(4 × 9) = √36 = 6.

The harmonic mean divides n by the sum of reciprocals and suits rates like average speed; for a trip at 40 and 60 mph over equal distances, the harmonic mean is 2 × 40 × 60 / (40 + 60) = 48 mph, and you can verify the travel times behind that result with a speed distance time calculator.

Wolfram MathWorld notes that for any set of positive numbers the harmonic mean never exceeds the geometric mean, which never exceeds the arithmetic mean. Choosing the right mean prevents misleading results.

Averages appear everywhere: teachers compute grade point averages, economists track average income, and analysts report average customer spend.

In finance, weighted averages summarize portfolio returns; in sports, batting and scoring averages compare athletes; in science, the mean of repeated measurements reduces random error.

Khan Academy highlights the median as the preferred average for skewed data such as home prices or salaries, because a few extreme values pull the mean upward. Standard deviation, reported alongside the mean, tells you how tightly data clusters around it.

Businesses also use moving averages to smooth noisy time-series data and reveal underlying trends over rolling periods.

The most common error is letting outliers distort the mean: for 2, 3, 4, 5, 100 the mean is 114 / 5 = 22.8, yet the median of 4 far better represents the typical value.

Another frequent mistake is averaging percentages or rates directly without weighting them by their base amounts. People also confuse mode (most frequent value) with mean, or forget that an even-sized data set has no single middle number, so the median is the average of the two central values.

Encyclopaedia Britannica cautions that no single average fits every distribution. Finally, always match the number of weights to the number of values in a weighted average.