The mean deviation about the median of the nu | vedclass

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(D) First,arrange the given numbers in ascending order: $2, 3, 5, 7, 9, 11, 13, 15, 17, 20$. Since the number of observations $n = 10$ (which is even)

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) First,arrange the given numbers in ascending order: $2, 3, 5, 7, 9, 11, 13, 15, 17, 20$. Since the number of observations $n = 10$ (which is even),the median is the average of the $5^{th}$ and $6^{th}$ observations. Median $M = \frac{9 + 11}{2} = \frac{20}{2} = 10$. Now,calculate the absolute deviations from the median $|x_i - M|$: $|2 - 10| = 8, |3 - 10| = 7, |5 - 10| = 5, |7 - 10| = 3, |9 - 10| = 1, |11 - 10| = 1, |13 - 10| = 3, |15 - 10| = 5, |17 - 10| = 7, |20 - 10| = 10$. The sum of these absolute deviations is $8 + 7 + 5 + 3 + 1 + 1 + 3 + 5 + 7 + 10 = 50$. The mean deviation about the median is $\frac{1}{n} \sum |x_i - M| = \frac{50}{10} = 5$.

Class Interval	$0$–$2$	$2$–$4$	$4$–$6$	$6$–$8$	$8$–$10$
Frequency	$1$	$3$	$4$	$1$	$2$

$x_i$	$6$	$12$	$18$	$24$	$30$	$36$	$42$
$f_i$	$4$	$7$	$9$	$18$	$15$	$10$	$5$

Class Interval	$0-4$	$4-8$	$8-12$	$12-16$
Frequency	$4$	$3$	$2$	$1$

The mean deviation about the median of the numbers $2, 3, 5, 20, 17, 15, 13, 11, 9, 7$ is

Similar Questions

Find the mean deviation about the median for the data: $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$.

The mean deviation about the mean for the following data is
Class Interval $0$–$2$ $2$–$4$ $4$–$6$ $6$–$8$ $8$–$10$
Frequency $1$ $3$ $4$ $1$ $2$

For the following distribution,the mean deviation about the median is:
$x_i$ $6$ $12$ $18$ $24$ $30$ $36$ $42$
$f_i$ $4$ $7$ $9$ $18$ $15$ $10$ $5$

The mean deviation about the mean for the following data is

Class Interval $0-4$ $4-8$ $8-12$ $12-16$

Frequency $4$ $3$ $2$ $1$

Find the mean deviation about the mean for the data $4, 7, 8, 9, 10, 12, 13, 17$.

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