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(A) The given observations are already in ascending order. Adding a column corresponding to cumulative frequencies $(c.f.)$ of the given data,we obtai

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$3.23$

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(A) The given observations are already in ascending order. Adding a column corresponding to cumulative frequencies $(c.f.)$ of the given data,we obtain the following table:						${x_i}$			${f_i}$			$c.f.$							$5$			$8$			$8$							$7$			$6$			$14$							$9$			$2$			$16$							$10$			$2$			$18$							$12$			$2$			$20$							$15$			$6$			$26$			Here,$N = \sum f_i = 26,$ which is even.Median is the mean of the $13^{th}$ and $14^{th}$ observations. Both of these observations lie in the cumulative frequency $14,$ for which the corresponding observation is $7.$$	herefore 	ext{Median} (M) = \frac{7 + 7}{2} = 7.$The absolute values of the deviations from median,i.e.,$|x_i - M|,$ are calculated as follows:						$x_i$			$|x_i - M|$			$f_i$			$f_i|x_i - M|$							$5$			$2$			$8$			$16$							$7$			$0$			$6$			$0$							$9$			$2$			$2$			$4$							$10$			$3$			$2$			$6$							$12$			$5$			$2$			$10$							$15$			$8$			$6$			$48$			$\sum f_i |x_i - M| = 16 + 0 + 4 + 6 + 10 + 48 = 84.$$	ext{Mean Deviation} (M) = \frac{1}{N} \sum f_i |x_i - M| = \frac{84}{26} \approx 3.23.$

Find the mean deviation about the median for the data.

${x_i}$ $5$ $7$ $9$ $10$ $12$ $15$

${f_i}$ $8$ $6$ $2$ $2$ $2$ $6$

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Find the mean deviation about the median for the data. ${x_i}$ $5$ $7$ $9$ $10$ $12$ $15$ ${f_i}$ $8$ $6$ $2$ $2$ $2$ $6$