Measures of Dispersion for Grouped Data
Quartile
A value dividing ordered data into quarters; the first, second (median) and third quartiles.
| English | Quartile |
|---|---|
| Bahasa Melayu | Kuartil |
| 中文 | 四分位数 |
How it is used
With n = 30 data values, the first quartile is at position n/4 = 7.5 and the third at 3n/4 = 22.5 on the ogive. If reading gives Q1 = 16.9 and Q3 = 31.3, the interquartile range is Q3 − Q1 = 31.3 − 16.9 = 14.4.
Where it shows up in SPM
In grouped-data statistics, Form 5, Paper 2. After drawing an ogive you read Q1 at n/4 and Q3 at 3n/4 up the cumulative frequency axis, then find the interquartile range Q3 − Q1 as a measure of spread.
Quartiles may also be found by interpolation from the cumulative frequency table.
Don't confuse it with
Open the chapter: Measures of Dispersion for Grouped Data →
Frequently asked questions
What positions do Q1 and Q3 sit at?
On an ogive, read Q1 at cumulative frequency n/4 and Q3 at 3n/4. For n = 30 that is positions 7.5 and 22.5.
Draw across to the curve and down to the horizontal axis to read each quartile value.
How are quartiles used to measure spread?
Subtract Q1 from Q3 to get the interquartile range, which covers the middle half of the data. A smaller interquartile range means the values are more tightly clustered; a larger one means they are more spread out.