Midpoint of a Class Interval

Statement

The midpoint of a class interval in grouped data is found by:

\[ x_{\text{mid}} = \frac{\text{lower boundary} + \text{upper boundary}}{2} \]

Why it’s true

• In grouped frequency tables, values are given as ranges (class intervals).
• The midpoint represents a single value that best represents the entire interval.
• It is simply the average of the lower and upper boundaries.

Recipe (how to use it)

1. Identify the lower and upper boundary of the interval (e.g., 10–20).
2. Add them together.
3. Divide by 2 to find the midpoint.

Spotting it

You use midpoints whenever you need to calculate an estimated mean from grouped frequency tables.

Common pairings

• Frequency tables with intervals.
• Estimating means.
• Statistical calculations when exact data isn’t given.

Mini examples

1. Class interval: 10–20. Midpoint = (10+20)/2 = 15.
2. Class interval: 30–40. Midpoint = (30+40)/2 = 35.

Pitfalls

• Using boundaries incorrectly: Use actual boundaries (e.g., 10–20 means 9.5–20.5 in some tables).
• Forgetting to divide by 2: Always take the average.
• Not using midpoints consistently: Needed for estimating means.

Exam strategy

• Always write the formula clearly: midpoint = (lower+upper)/2.
• Work systematically across all intervals.
• Check: midpoint should lie inside the interval.

Summary

The midpoint of a class interval is the average of its boundaries. Formula: \((\text{lower} + \text{upper})/2\). It represents the typical value for that interval.