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Mathematics

Find the median for the following distribution :

Wages per day (in ₹)No. of workers
3814
458
487
5510
626
652

Measures of Central Tendency

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Answer

The given variates (wages) are already in ascending order. We construct the cumulative frequency table as under :

Variate (Wages per day)Frequency (No. of workers)Cumulative frequency
381414
45822
48729
551039
62645
65247

Here, n (total no. of workers) = 47, which is odd.

Median=n+12th observation=47+12=482=24th observation\therefore \text{Median} = \dfrac{n + 1}{2} \text{th observation} \\[1em] = \dfrac{47 + 1}{2} \\[1em] = \dfrac{48}{2} \\[1em] = 24 \text{th observation}

All observations from 23rd to 29th are equal, each = 48.

Hence, median = ₹48.

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