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 observations are already in ascending order.Adding a column for cumulative frequencies $(c.f.)$:						$x_i$			$f_i$			$c.f.$							$15$

Vedclass · Accepted Answer

$5.10$

Vedclass · Answer

(A) The given observations are already in ascending order.Adding a column for cumulative frequencies $(c.f.)$:						$x_i$			$f_i$			$c.f.$							$15$			$3$			$3$							$21$			$5$			$8$							$27$			$6$			$14$							$30$			$7$			$21$							$35$			$8$			$29$			Here,$N = \sum f_i = 29$,which is odd.Median $= \left(\frac{N+1}{2}\right)^{th}$ observation $= \left(\frac{29+1}{2}\right)^{th} = 15^{th}$ observation.This observation lies in the cumulative frequency $21$,for which the corresponding value is $x_i = 30$.So,Median $(M) = 30$.Calculating $|x_i - M|$ and $f_i|x_i - M|$:						$x_i$			$f_i$			$|x_i - 30|$			$f_i|x_i - 30|$							$15$			$3$			$15$			$45$							$21$			$5$			$9$			$45$							$27$			$6$			$3$			$18$							$30$			$7$			$0$			$0$							$35$			$8$			$5$			$40$			Sum $\sum f_i|x_i - M| = 45 + 45 + 18 + 0 + 40 = 148$.Mean Deviation about Median $= \frac{1}{N} \sum f_i|x_i - M| = \frac{148}{29} \approx 5.10$.

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

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

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

Similar Questions

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

What is the coefficient of mean deviation about the median for the observations $40, 62, 54, 90, 68, 76$?

Find the mean deviation about the median for the data.

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

${f_i}$ $8$ $6$ $2$ $2$ $2$ $6$

If the mean of $4, 7, 2, 8, 6$ and $a$ is $7$,find the mean deviation about the median of these observations.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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

Find the mean deviation about the median for the given data: $x_i$ $15$ $21$ $27$ $30$ $35$ $f_i$ $3$ $5$ $6$ $7$ $8$