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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

$4$

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

Size $(x)$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$
Frequency $(f)$	$3$	$3$	$4$	$14$	$7$	$4$	$3$	$4$

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

Class interval	$0$-$10$	$10$-$20$	$20$-$30$	$30$-$40$	$40$-$50$	$50$-$60$	$60$-$70$
Frequency	$4$	$6$	$16$	$28$	$16$	$6$	$4$

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

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

If $M_1$ is the mean deviation from the mean of the discrete data $44, 5, 27, 20, 8, 54, 9, 14, 35$ and $M_2$ is the mean deviation from the median of the same data,then $M_1 - M_2 =$

The mean deviation about the mean of the following data is nearly:
Size $(x)$ $1$ $3$ $5$ $7$ $9$ $11$ $13$ $15$
Frequency $(f)$ $3$ $3$ $4$ $14$ $7$ $4$ $3$ $4$

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 mean for the following data:
Class interval $0$-$10$ $10$-$20$ $20$-$30$ $30$-$40$ $40$-$50$ $50$-$60$ $60$-$70$
Frequency $4$ $6$ $16$ $28$ $16$ $6$ $4$

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