Calculate the arithmetic mean, median, sum, count, variance, and standard deviation for any dataset with step-by-step steps.
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The arithmetic mean (commonly called the average) is the central tendency measure calculated by dividing the sum of a collection of numbers by the total count of numbers in the collection.
\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i = \frac{x_1 + x_2 + \dots + x_n}{n}Sum all values x_i in the dataset, then divide by the sample size n.
Scenario: Find the arithmetic mean of 12, 18, 25, 30, 40
Count items: n = 5
Sum items: Σx = 12 + 18 + 25 + 30 + 40 = 125
Compute mean: x̄ = 125 / 5 = 25
Median: The middle value in sorted order is 25
In general speech, average refers to the arithmetic mean. In statistics, average can refer to any measure of central tendency including mean, median, or mode.
Because the mean incorporates every value equally, unusually large or small values will pull the mean toward the extreme, potentially distorting the representative center.
Sample mean (x̄) is computed from a subset of a population, while population mean (μ) is the true mean of all members in the entire population.
Yes, if the sum of the numbers in the dataset is negative, the resulting arithmetic mean will be negative.
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