If the mean deviation about the mean of the n | vedclass

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

Question

(A) The given numbers are in an arithmetic progression: $1, 1+d, 1+2d, \dots, 1+100d$. Here,the number of terms is $N = 101$. The mean of these terms

Vedclass · Accepted Answer

$10.1$

Vedclass · Answer

(A) The given numbers are in an arithmetic progression: $1, 1+d, 1+2d, \dots, 1+100d$. Here,the number of terms is $N = 101$. The mean of these terms is $\bar{x} = \frac{1}{101} \sum_{i=0}^{100} (1 + id) = 1 + \frac{d}{101} 	imes \frac{100 	imes 101}{2} = 1 + 50d$. The mean deviation about the mean is given by $M.D. = \frac{1}{N} \sum_{i=0}^{100} |(1+id) - (1+50d)| = \frac{1}{101} \sum_{i=0}^{100} |(i-50)d| = \frac{|d|}{101} \sum_{i=0}^{100} |i-50|$. Calculating the sum: $\sum_{i=0}^{100} |i-50| = (50+49+\dots+1) + 0 + (1+2+\dots+50) = 2 	imes \frac{50 	imes 51}{2} = 2550$. Thus,$M.D. = \frac{|d|}{101} 	imes 2550 = 255$. $|d| = \frac{255 	imes 101}{2550} = \frac{101}{10} = 10.1$.

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

$x_i$	$2$	$4$	$6$	$8$	$10$
$f_i$	$1$	$2$	$3$	$2$	$1$

If the mean deviation about the mean of the numbers $1, 1 + d, 1 + 2d, \dots, 1 + 100d$ is $255$,then what is the value of $|d|$?

Similar Questions

The following data represents the frequency distribution of $20$ observations.
$x_i$ $3$ $4$ $5$ $8$ $10$ $11$
$f_i$ $\alpha+2$ $(\alpha-1)^2$ $4$ $\alpha-1$ $2$ $\alpha$
Then its mean deviation about the mean is

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 /$13$)

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

If the mean deviation about the mean of the numbers $1, 2, 3, \ldots, n$,where $n$ is odd,is $\frac{5(n+1)}{n}$,then $n$ is equal to

Consider the following distribution:
$x_i$ $2$ $4$ $6$ $8$ $10$
$f_i$ $1$ $2$ $3$ $2$ $1$

The sum of the mean deviation from the mean and the mean deviation from the median of this distribution is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module