Hey there! I totally get why these terms can feel fuzzy—they’re often used interchangeably in casual explanations, but let’s break them down with plain, concrete examples so you won’t mix them up again.

First, the Definitions (With a Simple Example) #

Let’s use a common grouped data set: test scores grouped into ranges like 50-60, 60-70, 70-80.

• Class Interval
  This is the actual range of values that defines a group. Using our example, 50-60 is a class interval—it’s the set of all scores from 50 up to (but not always including) 60. Think of it as the "bucket" label that tells you which values belong in that group. It’s a range, not a single number.

• Class Width
  This is the numerical length of the class interval. For 50-60, subtract the lower limit from the upper limit: 60 - 50 = 10. That’s the class width—it’s how "wide" the bucket is, a single number.

• Class Size
  Here’s the gotcha: most of the time, this is exactly the same as class width. Many textbooks and instructors use the two terms interchangeably to mean the length of the interval.
  That said, in a tiny number of contexts, someone might use "class size" to refer to the number of data points (frequency) that fall into the class interval (like if 12 students scored between 50-60, the class size could be 12). But this usage is rare—stick with assuming it’s synonymous with class width unless told otherwise.

What Does the Symbol $i$ Refer To? #

In grouped statistics notation, the symbol $i$ almost always stands for class width (or class size, since they’re usually the same). You’ll see it used in formulas like calculating the midpoint of a class interval:
Midpoint = (Lower Limit + Upper Limit) / 2
Or when calculating estimated mean from grouped data, where $i$ is the width you use to scale deviations from the assumed mean.

内容的提问来源于stack exchange，提问作者user484792