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Economics · Ch 5 — Measures of Central Tendency

Calculation of Quartiles

5.4.2

Calculation of Quartiles

Quartiles are located just like the median. For individual and discrete series the positions are given (with NN = number of observations) by:

Q1=size of (N+14)th item,Q3=size of (3(N+1)4)th itemQ_1 = \text{size of } \left(\frac{N+1}{4}\right)^{\text{th}} \text{ item}, \qquad Q_3 = \text{size of } \left(\frac{3(N+1)}{4}\right)^{\text{th}} \text{ item}

When the position is not a whole number, interpolate between the two adjacent items.

Example — lower quartile. Marks of ten students: 22, 26, 14, 30, 18, 11, 35, 41, 12, 32. Arranged in ascending order: 11, 12, 14, 18, 22, 26, 30, 32, 35, 41.

Q1=size of (N+14)th item=(10+14)th=2.75th itemQ_1 = \text{size of } \left(\frac{N+1}{4}\right)^{\text{th}} \text{ item} = \left(\frac{10+1}{4}\right)^{\text{th}} = 2.75^{\text{th}} \text{ item}

Interpolating between the 2nd and 3rd items:

Q1=2nd item+0.75 (3rd−2nd)=12+0.75(14−12)=13.5 marksQ_1 = 2^{\text{nd item}} + 0.75\,(3^{\text{rd}} - 2^{\text{nd}}) = 12 + 0.75(14 - 12) = 13.5 \text{ marks} …

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