The mean deviation from the median of the dat | vedclass

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Question

(C) Given data: $16, 22, 3, 14, 5, 10, 8, 6, 11, 4$. Arranging in ascending order: $3, 4, 5, 6, 8, 10, 11, 14, 16, 22$. Number of observations $n = 10

Vedclass · Accepted Answer

$4.7$

Vedclass · Answer

(C) Given data: $16, 22, 3, 14, 5, 10, 8, 6, 11, 4$. Arranging in ascending order: $3, 4, 5, 6, 8, 10, 11, 14, 16, 22$. Number of observations $n = 10$. Since $n$ is even,the median is the average of the $5^{	ext{th}}$ and $6^{	ext{th}}$ observations: $	ext{Median} = \frac{8 + 10}{2} = 9$. Mean deviation from the median is given by $\frac{1}{n} \sum |x_i - 	ext{Median}|$: $	ext{Mean Deviation} = \frac{|3-9| + |4-9| + |5-9| + |6-9| + |8-9| + |10-9| + |11-9| + |14-9| + |16-9| + |22-9|}{10}$ $= \frac{6 + 5 + 4 + 3 + 1 + 1 + 2 + 5 + 7 + 13}{10}$ $= \frac{47}{10} = 4.7$.

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

$x_i$	$15$	$21$	$27$	$30$	$35$
$f_i$	$3$	$5$	$6$	$7$	$8$

$x_i$	$3$	$6$	$9$	$12$	$13$	$15$	$21$	$22$
$f_i$	$3$	$4$	$5$	$2$	$4$	$5$	$4$	$3$

The mean deviation from the median of the data $16, 22, 3, 14, 5, 10, 8, 6, 11, 4$ is

Similar Questions

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 $2$ $3$ $8$ $14$ $8$ $3$ $2$

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

$x_i$ $15$ $21$ $27$ $30$ $35$

$f_i$ $3$ $5$ $6$ $7$ $8$

The mean deviation from the mean for the data $6, 7, 10, 12, 13, 4, 12, 16$ is

The mean deviation from the median is

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

$x_i$ $3$ $6$ $9$ $12$ $13$ $15$ $21$ $22$

$f_i$ $3$ $4$ $5$ $2$ $4$ $5$ $4$ $3$

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