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Class Interval — Definition, Formula & Examples

A class interval is a range of values that defines one group (or "class") in a grouped frequency distribution. For example, the class interval 10–19 includes all data values from 10 up to 19.

In a grouped frequency distribution, a class interval is a contiguous, non-overlapping subrange of the data's domain, characterized by a lower class boundary and an upper class boundary. The width of each class interval equals the difference between successive lower boundaries.

Key Formula

w=max−minkw = \frac{\text{max} - \text{min}}{k}
Where:
  • ww = Class width (round up to a convenient whole number)
  • max\text{max} = Largest value in the data set
  • min\text{min} = Smallest value in the data set
  • kk = Number of classes (groups) you want

How It Works

To build class intervals, first find the range of your data set (maximum minus minimum). Then decide how many classes you want — typically between 5 and 20. Divide the range by the number of classes to get the class width, rounding up to a convenient number. Starting at or just below the minimum value, create intervals of equal width that cover the entire data set without overlapping. Each data value falls into exactly one interval.

Worked Example

Problem: A teacher records 20 test scores ranging from 42 to 98. She wants to organize them into 6 class intervals. Find the class width and list the intervals.
Find the range: Subtract the minimum from the maximum.
98−42=5698 - 42 = 56
Calculate width: Divide the range by the number of classes, then round up.
w=566≈9.33  ⇒  w=10w = \frac{56}{6} \approx 9.33 \;\Rightarrow\; w = 10
List the intervals: Start at 40 (a convenient number at or below the minimum) and add the width repeatedly.
40–49,  50–59,  60–69,  70–79,  80–89,  90–9940\text{–}49,\; 50\text{–}59,\; 60\text{–}69,\; 70\text{–}79,\; 80\text{–}89,\; 90\text{–}99
Answer: Six class intervals of width 10: 40–49, 50–59, 60–69, 70–79, 80–89, and 90–99.

Visualization

Why It Matters

Histograms and frequency tables both depend on well-chosen class intervals. In AP Statistics and introductory college courses, you will use them to summarize large data sets, spot distribution shapes, and identify outliers quickly.

Common Mistakes

Mistake: Creating overlapping intervals like 10–20 and 20–30, so the value 20 could be counted in two classes.
Correction: Use non-overlapping boundaries such as 10–19 and 20–29, or use precise notation like 10 ≤ x < 20 and 20 ≤ x < 30, so every value belongs to exactly one class.