The summation symbol (∑) is a mathematical notation that represents the sum of a series of values. It comes from the Greek capital letter sigma and is read as “the sum of.” The symbol provides a compact way to express the addition of many numbers, especially when they follow a pattern.
A typical summation expression looks like this:
This tells you to add up all the values of x from i = 1 to n. Here’s what each part means:
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∑: The summation symbol, meaning “sum.”
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i = 1: The index of summation, showing where to start (in this case, at i = 1).
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n: The number where the index stops (e.g., i goes from 1 to n).
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xᵢ: The general term being summed, often based on the index i.
The summation symbol is widely used in statistics, calculus, and algebra to write formulas more efficiently. In statistics, it often appears in formulas for the mean, variance, or regression—any time multiple data values are being combined.
For example, to calculate the mean of five numbers, you can write:
This summation formula means you add up the five values of x, then multiply the total by 1/5 to get the average—because multiplying by 1/5 is the same as dividing by 5.
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