Engineering
Mathematics
Measure of Dispersion
Question
If the mean deviation about the median of the numbers a, 2a, .......50a is 50, then |a| equals :
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Solution
Median = 25.5a
Mean deviation about median = 50
Þ \(\frac{{\Sigma |{x_i} - 25 \cdot 5a|}}{{50}} = 50\)
Þ 24.5 a + 23.5a + ..... + 0.5a + 0.5a + .... + 24.5a = 2500
Þ a + 3a + 5a + ..... + 49a = 2500
Þ \(\frac{{25}}{2}\)(50a) = 2500 Þ a = 4