Find the mean deviation about the median for | vedclass

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(C) First,arrange the observations in ascending order: $150, 210, 240, 300, 310, 320, 340$.The number of observations $n = 7$,which is odd.The median

Vedclass · Accepted Answer

$52.8$

Vedclass · Answer

(C) First,arrange the observations in ascending order: $150, 210, 240, 300, 310, 320, 340$.The number of observations $n = 7$,which is odd.The median is the middle term,which is the $4^{th}$ term: $	ext{Median} = 300$.Now,calculate the mean deviation about the median using the formula $\frac{1}{n} \sum |x_i - 	ext{Median}|$: 						$x_i$			$|x_i - 300|$							$150$			$|150 - 300| = 150$							$210$			$|210 - 300| = 90$							$240$			$|240 - 300| = 60$							$300$			$|300 - 300| = 0$							$310$			$|310 - 300| = 10$							$320$			$|320 - 300| = 20$							$340$			$|340 - 300| = 40$							Total			$\sum |x_i - 300| = 370$			Mean deviation about median $= \frac{370}{7} \approx 52.857 \approx 52.86$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Freq	$6$	$7$	$15$	$16$	$4$	$2$

Find the mean deviation about the median for the given data: $340, 150, 210, 240, 300, 310, 320$.

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