Class boundaries are essential in frequency distributions to prevent overlapping between adjacent classes, especially when data is continuous. Here's a clear example:

Example:

Suppose we are constructing a frequency distribution for the following exam scores (in percentages) out of 100:

Scores: 45, 52, 57, 60, 62, 67, 72, 75, 80, 85, 87, 90, 92, 95

We will create classes of width 10. The class intervals might look like this:

Class Interval	Frequency
40–50	1
50–60	2
60–70	3
70–80	2
80–90	3
90–100	3

However, there is a potential problem with the class intervals above. For example, a score of exactly 50 could either fall into the "40–50" class or the "50–60" class. To avoid this overlap, we use class boundaries.

Applying Class Boundaries:

We adjust the intervals slightly to ensure no overlap by introducing class boundaries. In this case, we subtract 0.5 from the lower limit and add 0.5 to the upper limit.

Class Interval	Class Boundaries	Frequency
40–50	39.5–50.5	1
50–60	50.5–60.5	2
60–70	60.5–70.5	3
70–80	70.5–80.5	2
80–90	80.5–90.5	3
90–100	90.5–100.5	3

Now, a score of exactly 50 falls within the 39.5–50.5 range and is counted in the first class without any ambiguity, and similarly for other class boundaries.

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Would you like more detailed steps on constructing this frequency table, or have any questions?

Related Questions:

1. How are class limits different from class boundaries?
2. Why are class boundaries needed for continuous data but not for discrete data?
3. What are other techniques to avoid overlap in data classification?
4. How can class boundaries be applied in a histogram?
5. How do class boundaries affect the calculation of cumulative frequencies?

Tip:

Always ensure class boundaries are clearly defined when working with continuous data to prevent ambiguity in class assignments.