Measures of Dispersion for Grouped Data
Interpolation
Reading a value between plotted points, for example finding the median from an ogive.
| English | Interpolation |
|---|---|
| Bahasa Melayu | Interpolasi |
| 中文 | 内插 |
How it is used
For n = 30, the median is at position 15, which falls in the class 21–30 (lower boundary 20.5, cumulative frequency 10 before it, class frequency 12, width 10). By interpolation the median = 20.5 + [(15 − 10) ÷ 12] × 10 = 24.67.
Where it shows up in SPM
In grouped-data statistics, Form 5. Interpolation gives an exact-looking value for the median or a quartile from the cumulative frequency table without drawing a graph, using the formula L + [(n/2 − F) ÷ f] × c.
It is the algebraic alternative to reading these off an ogive in Paper 2.
Don't confuse it with
Open the chapter: Measures of Dispersion for Grouped Data →
Frequently asked questions
What does each letter in the interpolation formula mean?
In L + [(n/2 − F) ÷ f] × c, L is the lower boundary of the median class, n is the total frequency, F is the cumulative frequency before that class, f is the class's frequency and c is the class width. For a quartile, replace n/2 with n/4 or 3n/4.
How do I find which class the median is in?
Work out n/2, then look down the cumulative frequency column for the first class whose running total reaches or passes n/2. That is the median class, whose lower boundary you use as L in the formula.