If the mean deviation about the median for th | vedclass

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(D) The given data is $3, 5, 7, 2k, 12, 16, 21, 24$. The number of observations $n = 8$.Since $n$ is even,the median $M$ is the average of the $4^{th}

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(D) The given data is $3, 5, 7, 2k, 12, 16, 21, 24$. The number of observations $n = 8$.Since $n$ is even,the median $M$ is the average of the $4^{th}$ and $5^{th}$ terms: $M = \frac{2k + 12}{2} = k + 6$.Mean deviation about median is given by $\frac{1}{n} \sum |x_i - M| = 6$.Substituting the values: $\frac{|3-(k+6)| + |5-(k+6)| + |7-(k+6)| + |2k-(k+6)| + |12-(k+6)| + |16-(k+6)| + |21-(k+6)| + |24-(k+6)|}{8} = 6$.This simplifies to: $\frac{|-k-3| + |-k-1| + |-k+1| + |k-6| + |6-k| + |10-k| + |15-k| + |18-k|}{8} = 6$.Assuming $k$ is such that the terms maintain the order,the sum is $(k+3) + (k+1) + (k-1) + (6-k) + (6-k) + (10-k) + (15-k) + (18-k) = 58 - 2k$.$\frac{58 - 2k}{8} = 6 \implies 58 - 2k = 48 \implies 2k = 10 \implies k = 5$.Thus,the median $M = k + 6 = 5 + 6 = 11$.

Marks obtained	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Number of students	$10$	$8$	$12$	$9$	$11$

$x_i$	$5$	$7$	$9$	$10$	$12$	$15$
$f_i$	$8$	$6$	$2$	$2$	$2$	$6$

If the mean deviation about the median for the numbers $3, 5, 7, 2k, 12, 16, 21, 24$ arranged in ascending order is $6$,then the median is:

Similar Questions

If the mean deviation about the median of $x, 2x, 3x, 4x, 5x, 6x, 7x, 8x, 9x, 10x$ is $30$,then $|x|$ equals:

Find the mean deviation about the mean for the following data:
Marks obtained $0-20$ $20-40$ $40-60$ $60-80$ $80-100$
Number of students $10$ $8$ $12$ $9$ $11$

The mean deviation about the mean for the data:

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

$f_i$ $8$ $6$ $2$ $2$ $2$ $6$

is equal to: (in /$13$)

$\begin{aligned} &\text{Find the mean deviation about the mean for the following data:} \\ &\begin{array}{|l|c|c|c|c|c|} \hline \text{Class Interval} & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text{Frequency} & 1 & 2 & 3 & 2 & 1 \\ \hline \end{array} \end{aligned}$

Let the mean and the standard deviation of the observations $2, 3, 3, 4, 5, 7, a, b$ be $4$ and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is:

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