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 $\frac{1}{n} \sum |x_i - M| = \frac{50}{10} = 5$.

Marks obtained	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
No of students	$2$	$3$	$8$	$14$	$8$	$3$	$2$

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

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
No of Girls	$6$	$8$	$14$	$16$	$4$	$2$

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

Similar Questions

If the mean deviation about the median of the numbers $a, 2a, 3a, \dots, 50a$ is $50$,then what is the value of $|a|$?

Find the mean deviation about the mean for the following data.
Marks obtained $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
No of students $2$ $3$ $8$ $14$ $8$ $3$ $2$

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

Find the mean deviation about the median for the following data:

Marks $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

No of Girls $6$ $8$ $14$ $16$ $4$ $2$

The mean deviation from the mean for the observations $1, 3, 5, 7, 11, 13, 17, 19, 23$ is

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