Measures of Dispersion for Grouped Data
Class midpoint
The middle value of a class interval, used to stand in for all values in that interval.
| English | Class midpoint |
|---|---|
| Bahasa Melayu | Titik tengah kelas |
| 中文 | 组中点 |
How it is used
For the class 21–30, the class midpoint is (21 + 30) ÷ 2 = 25.5. Using midpoints for every class and the formula x̄ = Σfx ÷ Σf, a table with frequencies 3, 7, 12, 6, 2 gives Σfx = 735 and Σf = 30, so the estimated mean is 735 ÷ 30 = 24.5.
Where it shows up in SPM
In grouped-data statistics, Form 5. It is the first step in most Paper 2 mean and standard deviation questions: because raw values are lost once data is grouped, each class midpoint stands in for every value in that class before you apply Σfx ÷ Σf or the variance formula.
Don't confuse it with
Open the chapter: Measures of Dispersion for Grouped Data →
Frequently asked questions
How do I find a class midpoint?
Add the lower and upper limits of the class and divide by two. For 41–50 the midpoint is (41 + 50) ÷ 2 = 45.5.
You get the same answer using the boundaries: (40.5 + 50.5) ÷ 2 = 45.5.
Why do we use midpoints instead of the real data?
Once data is grouped into classes, the individual values are no longer known. The midpoint is the fairest single estimate for each value in that class, which is why the mean and standard deviation you calculate are estimates, not exact figures.