Measures of Dispersion for Grouped Data
Ogive
A cumulative frequency curve, used to read off the median and quartiles of grouped data.
| English | Ogive |
|---|---|
| Bahasa Melayu | Ogif |
| 中文 | 累积频率曲线 |
How it is used
Plot cumulative frequency against the upper boundary of each class and join the points with a smooth curve. For n = 40 students, read across from cumulative frequency 20 to the curve, then down, to estimate the median; reading from 10 and 30 gives Q1 and Q3.
Where it shows up in SPM
In the Measures of Dispersion (grouped data) chapter, Form 5. A Paper 2 question typically gives a frequency table, asks you to complete a cumulative frequency column, draw the ogive on graph paper, then use it to estimate the median, the first and third quartiles and the interquartile range.
Don't confuse it with
Open the chapter: Measures of Dispersion for Grouped Data →
Frequently asked questions
What goes on each axis of an ogive?
Put the upper boundary of each class on the horizontal axis and the cumulative frequency on the vertical axis. Begin at the lower boundary of the first class with cumulative frequency 0, then plot each point and join them with a smooth curve.
How do I read the median from the ogive?
Find n/2 on the cumulative frequency axis; for n = 40 that is 20. Draw a horizontal line to the curve, then drop straight down to the horizontal axis.
The value you land on is the estimated median.
Why does an ogive never go down?
Because cumulative frequency is a running total: each class adds its frequency to the previous total, so the value can only stay the same or rise. The curve climbs steadily from 0 to n, which is the total frequency.