If M_1 is the mean deviation from the mean of | vedclass

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

Question

(D) The given data is $44, 5, 27, 20, 8, 54, 9, 14, 35$. The number of observations $N = 9$.First,calculate the mean $\bar{x} = \frac{44+5+27+20+8+54+

Vedclass · Accepted Answer

$\frac{4}{9}$

Vedclass · Answer

(D) The given data is $44, 5, 27, 20, 8, 54, 9, 14, 35$. The number of observations $N = 9$.First,calculate the mean $\bar{x} = \frac{44+5+27+20+8+54+9+14+35}{9} = \frac{216}{9} = 24$.The mean deviation about the mean $M_1 = \frac{1}{N} \sum |x_i - \bar{x}|$.$|44-24| + |5-24| + |27-24| + |20-24| + |8-24| + |54-24| + |9-24| + |14-24| + |35-24| = 20 + 19 + 3 + 4 + 16 + 30 + 15 + 10 + 11 = 128$.So,$M_1 = \frac{128}{9}$.Now,arrange the data in ascending order: $5, 8, 9, 14, 20, 27, 35, 44, 54$.The median $M$ is the $\left(\frac{9+1}{2}ight)^{	ext{th}} = 5^{	ext{th}}$ term,which is $20$.The mean deviation about the median $M_2 = \frac{1}{N} \sum |x_i - M|$.$|5-20| + |8-20| + |9-20| + |14-20| + |20-20| + |27-20| + |35-20| + |44-20| + |54-20| = 15 + 12 + 11 + 6 + 0 + 7 + 15 + 24 + 34 = 124$.So,$M_2 = \frac{124}{9}$.Therefore,$M_1 - M_2 = \frac{128}{9} - \frac{124}{9} = \frac{4}{9}$.

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

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

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 $M_1 - M_2 =$

Similar Questions

Find the mean deviation about the mean for the data $38, 70, 48, 40, 42, 55, 63, 46, 54, 44$.

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 $4$ $6$ $16$ $28$ $16$ $6$ $4$

What is the mean deviation about the mean for the observations $5, 10, 15, 20, \dots, 85$?

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 /$13$)

The mean deviation about the mean for the data $4, 7, 8, 9, 10, 12, 13, 17$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module