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

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(D) The mean of the first $n$ natural numbers is $\bar{x} = \frac{n+1}{2}$.The mean deviation about the mean is given by $\frac{1}{n} \sum_{i=1}^{n} |

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(D) The mean of the first $n$ natural numbers is $\bar{x} = \frac{n+1}{2}$.The mean deviation about the mean is given by $\frac{1}{n} \sum_{i=1}^{n} |x_i - \bar{x}|$.For odd $n$,the mean deviation about the mean of the first $n$ natural numbers is $\frac{n^2-1}{4n}$.Given that the mean deviation is $\frac{5(n+1)}{n}$,we set up the equation:$\frac{n^2-1}{4n} = \frac{5(n+1)}{n}$.Since $n^2-1 = (n-1)(n+1)$,we have:$\frac{(n-1)(n+1)}{4n} = \frac{5(n+1)}{n}$.Dividing both sides by $\frac{n+1}{n}$ (since $n 
eq -1$):$\frac{n-1}{4} = 5$.$n-1 = 20$.$n = 21$.

Income per day	Number of persons
$0-100$	$4$
$100-200$	$8$
$200-300$	$9$
$300-400$	$10$
$400-500$	$7$
$500-600$	$5$
$600-700$	$4$
$700-800$	$3$

Class interval	Frequency
$0-2$	$1$
$2-4$	$3$
$4-6$	$5$
$6-8$	$3$
$8-10$	$1$

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

Similar Questions

Let the mean and the standard deviation of the observations $2, 3, 3, 4, 5, 7, a, b$ be $4$ and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is:

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

Find the mean deviation about the mean for the following data:
Income per day Number of persons
$0-100$ $4$
$100-200$ $8$
$200-300$ $9$
$300-400$ $10$
$400-500$ $7$
$500-600$ $5$
$600-700$ $4$
$700-800$ $3$

The mean deviation about the mean for the following data is
Class interval Frequency
$0-2$ $1$
$2-4$ $3$
$4-6$ $5$
$6-8$ $3$
$8-10$ $1$

The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$,then the mean deviation from the mean of the data is:

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