Measures of Dispersion for Grouped Data
How to Find Q1, Q3 and the Interquartile Range from an Ogive
Use this when a cumulative frequency curve (ogive) is given or has been drawn for grouped data, and the question asks for the first quartile, third quartile, or interquartile range.
When to use it
Use this when a cumulative frequency curve (ogive) is given or has been drawn for grouped data, and the question asks for the first quartile, third quartile, or interquartile range.
The steps
- Find N, the total frequency, either sum the frequency column or read the highest cumulative frequency value at the top of the ogive.
- Calculate N/4 for Q1 and 3N/4 for Q3, these are the positions to locate on the cumulative frequency axis.
- For each value, draw a horizontal line from that point on the cumulative frequency axis across to where it meets the curve.
- From that meeting point, draw a vertical line down to the horizontal axis, and read off the value, this gives Q1 (from N/4) and Q3 (from 3N/4).
- Subtract to find the interquartile range: interquartile range = Q3 − Q1.
Formulae you may need
x̄ = Σfx / Σf
Given in the examσ2 = Σf(x−x̄)2 / Σf = Σfx2/Σf − x̄2
Given in the examσ = √Σf(x−x̄)2 / Σf = √Σfx2/Σf − x̄2
Given in the examFormula pages
Practise this in a KBAT problem
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