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class width — Definition, Formula & Examples

Class width is the size of each interval in a grouped frequency distribution, calculated as the difference between consecutive lower class boundaries (or equivalently, upper boundary minus lower boundary of any single class).

In a grouped frequency distribution, class width is the constant value w=Bupper−Blowerw = B_{\text{upper}} - B_{\text{lower}} for any class, where BupperB_{\text{upper}} and BlowerB_{\text{lower}} are the true upper and lower class boundaries. When classes are equally spaced, this equals the difference between the lower limits (or upper limits) of two consecutive classes.

Key Formula

w=Rangekw = \frac{\text{Range}}{k}
Where:
  • ww = Class width (round up to a convenient number)
  • Range\text{Range} = Maximum data value minus minimum data value
  • kk = Desired number of classes

How It Works

To find class width, subtract the lower boundary of a class from its upper boundary. When designing a frequency table from scratch, you can choose class width by dividing the range of the data set by the desired number of classes and rounding up. Equal class widths keep every bar in a histogram the same width, which makes visual comparison of frequencies straightforward.

Worked Example

Problem: A data set ranges from 10 to 70, and you want 6 classes. Find the class width and list the first two classes.
Find the range: Subtract the minimum from the maximum.
Range=70−10=60\text{Range} = 70 - 10 = 60
Divide by number of classes: Divide the range by the desired number of classes.
w=606=10w = \frac{60}{6} = 10
Build the first two classes: Start at the minimum value and add the class width repeatedly.
10–19,20–2910\text{–}19,\quad 20\text{–}29
Answer: The class width is 10. The first two classes are 10–19 and 20–29.

Why It Matters

Choosing an appropriate class width directly affects how a histogram looks and what patterns you can spot. Too narrow a width creates noisy bars; too wide a width hides variation. In AP Statistics and introductory data-science courses, selecting class width is one of the first decisions you make when summarizing raw data.

Common Mistakes

Mistake: Using the class limits instead of class boundaries, which can give a width that is one unit too small.
Correction: For the classes 10–19 and 20–29, the stated limits differ by 9 (19 − 10), but the true class width is 10 because the boundary of the first class extends to 19.5 and the next starts at 19.5. A quick check: subtract consecutive lower limits (20 − 10 = 10).

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