Denote the measurements of a quantitative data set as follows: x₁, x₂, x₃,$\dots$, x_n, where x₁ is the first measurement in the data set, x₂ is the second measurement in the data set, x₃ is the third measurement in the data set, $\dots$, and x_n is the nth (and last) measurement in the data set. Thus, if we have five measurements in a set of data, we will write x₁, x₂, x₃, x₄, x₅ to represent the measurements. If the actual numbers are 5, 3, 8, 5, and 4, we have $x_1=5$, $x_2=3$, $x_3=8$, $x_4=5$, and $x_5=4$.

Most of the formulas used in this text require a summation of numbers. For example, one sum is the sum of all the measurements in the data set, or $x_1+x_2+x_3+\cdots +x_n$. To shorten the notation, we use the symbol $\mathrm{\Sigma }$ for the summation—that is, $x_1+x_2+x_3+\cdots +x_n={\displaystyle \sum _{i=1}^n{x}_i}$. Verbally translate ${\displaystyle \sum _{i=1}^n{x}_i}$ as follows: “The sum of the measurements, whose typical member is x_i, beginning with the member x₁ and ending with the member x_n.”

Suppose, as in our earlier example, that $x_1=5$, $x_2=3$, $x_3=8$, $x_4=5$, and $x_5=4$. Then the sum of the five measurements, denoted ${\displaystyle \sum _{i=1}^n{x}_i}$, is obtained as follows:

Another important calculation requires that we square each measurement and then sum the squares. The notation for this sum is ${\displaystyle \sum _{i=1}^n{x}_i^2}$. For the preceding five measurements, we have

In general, the symbol following the summation sign represents the variable (or function of the variable) that is to be summed.