If the mean deviation about the median of the numbers k, 2k, 3k, ....., 1000k is 500, then k is equal to : [2026]

Question

If the mean deviation about the median of the numbers k, 2k, 3k, ....., 1000k is 500, then $k ²$ is equal to : [2026]

Smart Achievers · Accepted Answer

(2)

$∵$ $median = \frac{1001 k}{2} = X_{M}$

$∴$ $mean deviation about median = \frac{\sum | X_{i} - X_{M} |}{n}$

$= \frac{2 (\frac{k}{2} + \frac{3 k}{2} + \frac{5 k}{2} + \dots 500 terms)}{1000}$

$= \frac{2 \cdot \frac{k}{2} {(500)}^{2}}{1000}$

$= \frac{500 k}{2} = 500 (given)$

$∴$ $k = 2$

$∴$ $k^{2} = 4$

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