How to find x_i in statistics?

The meaning of x_i depends on how your data are presented.

1) Raw (Ungrouped) Data

x_i is the i-th observation in your list. Example: For data {7, 9, 12, 15}: x₁=7, x₂=9, x₃=12, x₄=15.

2) Discrete Frequency Table

The x_i are the distinct values, each paired with a frequency f_i.

Here, x₁=2, x₂=3, x₃=5.

3) Grouped (Continuous) Frequency Table

x_i is the class mark (midpoint) of the i-th class.

x_i = (lower class boundary + upper class boundary) / 2

Example classes: 10–20, 20–30, 30–40 ⇒ x₁=15, x₂=25, x₃=35.

For open-ended classes (e.g., “40 & above”), estimate the midpoint using the same class width as previous classes or a justified assumption. 

Why You Need x_i

Frequently used in formulas such as the mean of grouped data: x̄ = (∑ f_i x_i) / (∑ f_i).