What is the mean deviation about the mean of | vedclass

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(B) The number of terms in the series is $N = 2n + 1$.The mean $\bar{x}$ is given by $\bar{x} = \frac{a + (a + d) + (a + 2d) + \dots + (a + 2nd)}{2n +

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$\frac{n(n + 1)}{2n + 1} |d|$

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(B) The number of terms in the series is $N = 2n + 1$.The mean $\bar{x}$ is given by $\bar{x} = \frac{a + (a + d) + (a + 2d) + \dots + (a + 2nd)}{2n + 1}$.Using the sum of an arithmetic progression,$\bar{x} = \frac{1}{2n + 1} \left[ \frac{2n + 1}{2} (a + a + 2nd) \right] = a + nd$.The mean deviation about the mean is $MD = \frac{1}{N} \sum_{i=1}^{N} |x_i - \bar{x}|$.$\sum |x_i - \bar{x}| = |a - (a + nd)| + |(a + d) - (a + nd)| + \dots + |(a + 2nd) - (a + nd)|$$= |-nd| + |(1 - n)d| + \dots + |0| + \dots + |nd| = 2|d| [n + (n - 1) + \dots + 1] = 2|d| \frac{n(n + 1)}{2} = n(n + 1)|d|$.Therefore,$MD = \frac{n(n + 1)|d|}{2n + 1}$.

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

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

What is the mean deviation about the mean of the series $a, a + d, a + 2d, \dots, a + 2nd$?

Similar Questions

Find the mean deviation about the mean for the following data:
$6, 7, 10, 12, 13, 4, 8, 12$

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

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 median for the data.

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

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

If the mean deviation about the median of the numbers $a, 2a, 3a, \dots, 50a$ is $50$,then what is the value of $|a|$?

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