If the mean deviation of the numbers 1, 1 + d | vedclass

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

Question

(A) The given numbers are $1, 1+d, 1+2d, \dots, 1+100d$. This is an arithmetic progression with $n = 101$ terms.The mean $\bar{x}$ is given by:$\bar{x

Vedclass · Accepted Answer

$10.1$

Vedclass · Answer

(A) The given numbers are $1, 1+d, 1+2d, \dots, 1+100d$. This is an arithmetic progression with $n = 101$ terms.The mean $\bar{x}$ is given by:$\bar{x} = \frac{1}{101} \sum_{k=0}^{100} (1 + kd) = \frac{1}{101} [101 + d 	imes \frac{100 	imes 101}{2}] = 1 + 50d$.The mean deviation from the mean is:$MD = \frac{1}{101} \sum_{k=0}^{100} |(1 + kd) - (1 + 50d)| = \frac{1}{101} \sum_{k=0}^{100} |(k - 50)d| = \frac{|d|}{101} \sum_{k=0}^{100} |k - 50|$.Calculating the sum: $\sum_{k=0}^{100} |k - 50| = |0-50| + |1-50| + \dots + |50-50| + \dots + |100-50| = 50 + 49 + \dots + 0 + 1 + \dots + 50 = 2 	imes \frac{50 	imes 51}{2} = 2550$.Thus,$MD = \frac{|d|}{101} 	imes 2550 = 255$.$|d| = \frac{255 	imes 101}{2550} = \frac{101}{10} = 10.1$.

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

If the mean deviation of the numbers $1, 1 + d, . . . , 1 + 100d$ from their mean is $255,$ then a value of $d$ is

Similar Questions

If the mean deviation about the median of the numbers $a, 2a, 3a, \dots, 50a$ is $50$,then $|a|$ equals:

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 $|d|$?

If $a_0, a_1, \ldots, a_{11}$ are in an arithmetic progression with common difference $d$,then their mean deviation from their arithmetic mean is

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

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

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

If $m$ and $M$ denote the mean deviations about the mean and about the median respectively of the data $20, 5, 15, 2, 7, 3, 11$,then the mean deviation about the mean of $m$ and $M$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module