Measures of Dispersion for Grouped Data
Class midpoint
The value halfway across a class interval, used to estimate the mean of grouped data.
| English | Class midpoint |
|---|---|
| Bahasa Melayu | Titik tengah kelas |
| 中文 | 组中点 |
How it is used
The class 31–40 has midpoint (31 + 40) ÷ 2 = 35.5. Multiplying each class midpoint by its frequency and using x̄ = Σfx ÷ Σf estimates the mean; for frequencies 3, 7, 12, 6, 2 this gives 735 ÷ 30 = 24.5.
Where it shows up in SPM
In grouped-data statistics, Form 5. The class midpoint is the x-value in the mean and standard deviation formulas for grouped data, x̄ = Σfx ÷ Σf.
In Paper 2 you add an x column of midpoints to the table, then an fx (and often fx²) column, before computing the answer.
Don't confuse it with
Open the chapter: Measures of Dispersion for Grouped Data →
Frequently asked questions
Do I use limits or boundaries to find the midpoint?
Either works and both give the same answer. For 31–40 the limits give (31 + 40) ÷ 2 = 35.5, and the boundaries give (30.5 + 40.5) ÷ 2 = 35.5.
Choose whichever numbers are already in front of you.
Why is the mean from midpoints only an estimate?
Because grouping hides the exact values, so the midpoint stands in for all of them. Real values may sit anywhere in the class, so Σfx ÷ Σf gives an estimated mean rather than the true mean of the original data.