Find the mean deviation about the median for | vedclass

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(A) The number of observations $n = 11$,which is odd.Arranging the data in ascending order: $3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21$.Median $(M) = \left

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) The number of observations $n = 11$,which is odd.Arranging the data in ascending order: $3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21$.Median $(M) = \left(\frac{n+1}{2}ight)^{	ext{th}}$ observation $= 6^{	ext{th}}$ observation $= 9$.The absolute deviations $|x_i - M|$ are:$|3-9|=6, |3-9|=6, |4-9|=5, |5-9|=4, |7-9|=2, |9-9|=0, |10-9|=1, |12-9|=3, |18-9|=9, |19-9|=10, |21-9|=12$.Sum of absolute deviations $\sum |x_i - M| = 6 + 6 + 5 + 4 + 2 + 0 + 1 + 3 + 9 + 10 + 12 = 58$.Mean Deviation about median $= \frac{1}{n} \sum |x_i - M| = \frac{58}{11} \approx 5.27$.

Class interval	Frequency
$0-2$	$1$
$2-4$	$3$
$4-6$	$5$
$6-8$	$3$
$8-10$	$1$

Find the mean deviation about the median for the following data: $3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21$ (in $.27$)

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