Arithmetic Mean
The average of a data set.
Formula
Variables
Example
The mean of 2, 4, 9 is (2+4+9)/3 = 5.
How it works
The arithmetic mean is found by adding all the data values and then dividing by how many values there are. This works because the total amount is being shared equally across every item, so each value gets the same "fair share" of the whole. It is a good way to represent a typical value when the data are spread out without extreme outliers dominating the result.
When to use it
Use this formula when you want one number to summarize a set of measurements, such as test scores, temperatures, or survey results. It is especially useful when every value should count equally toward the overall average.
Worked example, step by step
Find the mean of 6, 8, 10, and 12. Step 1: Write the formula: x̄ = (1/n)Σx_i Step 2: Count the values: n = 4 Step 3: Add the values: 6 + 8 + 10 + 12 = 36 Step 4: Divide by the number of values: 36 ÷ 4 = 9 Final answer: x̄ = 9
Common mistakes to avoid
- Forgetting to divide by the number of data values after adding them
- Using the wrong count for n, especially when a value is repeated or missing
- Confusing the mean with the median or the mode
Did You Know?
The mean is the balance point of the data — the spot where the distribution would perfectly seesaw.
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