Find the mean deviation about the median for | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given data is $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$.Here,the number of observations is $n = 12$,which is even.Arranging the data in

Vedclass · Accepted Answer

$2.33$

Vedclass · Answer

(A) The given data is $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$.Here,the number of observations is $n = 12$,which is even.Arranging the data in ascending order,we obtain:$10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18$.Median $M = \frac{(\frac{n}{2})^{th} 	ext{ observation} + (\frac{n}{2} + 1)^{th} 	ext{ observation}}{2} = \frac{6^{th} 	ext{ observation} + 7^{th} 	ext{ observation}}{2} = \frac{13 + 14}{2} = 13.5$.The absolute deviations $|x_i - M|$ are:$|10 - 13.5| = 3.5$$|11 - 13.5| = 2.5$$|11 - 13.5| = 2.5$$|12 - 13.5| = 1.5$$|13 - 13.5| = 0.5$$|13 - 13.5| = 0.5$$|14 - 13.5| = 0.5$$|16 - 13.5| = 2.5$$|16 - 13.5| = 2.5$$|17 - 13.5| = 3.5$$|17 - 13.5| = 3.5$$|18 - 13.5| = 4.5$Sum of absolute deviations = $3.5 + 2.5 + 2.5 + 1.5 + 0.5 + 0.5 + 0.5 + 2.5 + 2.5 + 3.5 + 3.5 + 4.5 = 28$.Mean deviation about median = $\frac{\sum |x_i - M|}{n} = \frac{28}{12} \approx 2.33$.

Age	$15$	$16$	$17$	$18$	$19$	$20$
No. of students	$5$	$8$	$5$	$12$	$X$	$Y$

Find the mean deviation about the median for the data: $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$.

Similar Questions

The frequency distribution of the age of students in a class of $40$ students is given below.

Age $15$ $16$ $17$ $18$ $19$ $20$

No. of students $5$ $8$ $5$ $12$ $X$ $Y$

If the mean deviation about the median is $1.25$,then $4X + 5Y$ is equal to:

If the mean of $4, 7, 2, 8, 6$ and $a$ is $7$,then the mean deviation from the median of these observations is

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

The mean deviation from the mean of the series $(a), (a+d), (a+2d), \ldots, (a+2nd)$ is

If $10$ is the mean of the data $2, 3, 5, 18, 17, 15, 13, x, 9, 7$,then the mean deviation of this data about its mean is

Vedclass Test Series

Exam Paper Generator

Online Exam Module