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(B) The given numbers are $a, 2a, 3a, \dots, 50a$. The total number of terms is $n = 50$.Since $n$ is even,the median is the average of the $25^{th}$

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The given numbers are $a, 2a, 3a, \dots, 50a$. The total number of terms is $n = 50$.Since $n$ is even,the median is the average of the $25^{th}$ and $26^{th}$ terms:$	ext{Median} = \frac{25a + 26a}{2} = 25.5a$.Mean deviation about the median is given by $\frac{1}{n} \sum_{i=1}^{n} |x_i - 	ext{Median}| = 50$.$\frac{1}{50} \sum_{i=1}^{50} |ia - 25.5a| = 50$.$\sum_{i=1}^{50} |i - 25.5| |a| = 2500$.$|a| (|25.5 - 1| + |25.5 - 2| + \dots + |25.5 - 50|) = 2500$.$|a| (24.5 + 23.5 + \dots + 0.5 + 0.5 + \dots + 24.5) = 2500$.$|a| 	imes 2 	imes (0.5 + 1.5 + \dots + 24.5) = 2500$.$|a| 	imes 2 	imes \frac{25}{2} (0.5 + 24.5) = 2500$.$|a| 	imes 25 	imes 25 = 2500$.$|a| 	imes 625 = 2500$.$|a| = 4$.

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

Class interval	$0-6$	$6-12$	$12-18$	$18-24$	$24-30$
Frequency	$4$	$5$	$3$	$6$	$2$

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

If the mean deviation about the median of the numbers $a, 2a, 3a, \dots, 50a$ is $50$,then $|a|$ equals:

Similar Questions

The mean deviation about the median for the observations $70, 42, 63, 34, 44, 54, 55, 46, 38, 48$ is:

The mean deviation about the mean for the following data is
Class interval Frequency
$0-2$ $1$
$2-4$ $3$
$4-6$ $5$
$6-8$ $3$
$8-10$ $1$

Find the mean deviation about the mean for the data $38, 70, 48, 40, 42, 55, 63, 46, 54, 44$.

Calculate the mean deviation from the median of the following data:
Class interval $0-6$ $6-12$ $12-18$ $18-24$ $24-30$
Frequency $4$ $5$ $3$ $6$ $2$

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

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