Calculate the arithmetic mean (average) of a list of numbers with sum, count, minimum, and maximum.
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18
Mean
108
Sum
6
Count
| Mean | 18 |
| Sum | 108 |
| Count | 6 |
| Minimum | 4 |
| Maximum | 42 |
Also in Statistics
Descriptive Statistics
The arithmetic mean (average) is the most widely used measure of central tendency. It is the sum of all values divided by the count of values. The mean is the balance point of a distribution — the value at which the total positive deviations equal the total negative deviations.
Mean = (x₁ + x₂ + … + xₙ) / n. Add all values and divide by how many there are. For [4, 8, 15, 16, 23, 42], the sum is 108 and the count is 6, so the mean is 108 / 6 = 18.
The mean is sensitive to every value in the dataset. Adding one very large or very small value pulls the mean significantly. This is why the mean is sometimes called a non-robust statistic. For skewed distributions or data with outliers, the median is often a better measure of the "typical" value.
In a perfectly symmetric distribution, the mean, median, and mode are equal. In a right-skewed distribution (long tail on the right), the mean is pulled upward above the median. In a left-skewed distribution, the mean falls below the median. This is why income data is usually summarised by the median (the middle earner) rather than the mean (inflated by a few very high earners).
The mode is the most common value. For a dataset with one clear peak, mode ≤ median ≤ mean holds for right-skewed data. All three together tell a much richer story than any single statistic alone.
The population mean (μ) is the mean of every member of the group you are studying. The sample mean (x̄) is the mean of a subset. Both are calculated the same way (sum divided by count), but they have different notations and different implications: the sample mean is an estimate of the population mean, subject to sampling error.
Frequently asked questions
Use the mean when your data is roughly symmetric and has no extreme outliers — it uses all the information in the data. Use the median when the data is skewed, has outliers, or is ordinal. Income, house prices, and response times are commonly reported as medians because a few very large values would make the mean misleadingly high.
No. The mean is always between the minimum and maximum values of the dataset. It is a weighted balance point, so it must lie within the range.
The ordinary arithmetic mean treats all values equally. A weighted mean multiplies each value by a weight before summing, then divides by the total weight. Course grade averages with different credit-hour weights are a common example: Weighted mean = Σ(value × weight) / Σweight.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Find the mean, median, mode, and range of any dataset. Handles multimodal and no-mode cases with count, sum, minimum, and maximum.
Find the median of a dataset, with handling for even-count sets by averaging the two middle values, plus count, min, max, and mean.
Calculate sample or population standard deviation, variance, mean, and summary values from a list of numbers.
Calculate sample or population variance and standard deviation from a list of numbers, with mean, count, sum, and range.
