When a die is rolled 42 times, it is observed | vedclass

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(A) The frequency distribution is given by $f_i = 2i$ for $x_i = i$ where $i \in \{1, 2, 3, 4, 5, 6\}$.$x_i$$1$$2$$3$$4$$5$$6$$f_i$$2$$4$$6$$8$$10$$12

Vedclass · Accepted Answer

$\frac{80}{63}$

Vedclass · Answer

(A) The frequency distribution is given by $f_i = 2i$ for $x_i = i$ where $i \in \{1, 2, 3, 4, 5, 6\}$.$x_i$$1$$2$$3$$4$$5$$6$$f_i$$2$$4$$6$$8$$10$$12$Total frequency $N = \sum f_i = 2(1+2+3+4+5+6) = 2(21) = 42$.Mean $\bar{x} = \frac{\sum f_i x_i}{N} = \frac{2(1^2+2^2+3^2+4^2+5^2+6^2)}{42} = \frac{2(91)}{42} = \frac{182}{42} = \frac{13}{3}$.Mean deviation from mean $MD = \frac{\sum f_i |x_i - \bar{x}|}{N}$.$MD = \frac{2|1-\frac{13}{3}| + 4|2-\frac{13}{3}| + 6|3-\frac{13}{3}| + 8|4-\frac{13}{3}| + 10|5-\frac{13}{3}| + 12|6-\frac{13}{3}|}{42}$.$MD = \frac{2(\frac{10}{3}) + 4(\frac{7}{3}) + 6(\frac{4}{3}) + 8(\frac{1}{3}) + 10(\frac{2}{3}) + 12(\frac{5}{3})}{42}$.$MD = \frac{20 + 28 + 24 + 8 + 20 + 60}{3 	imes 42} = \frac{160}{126} = \frac{80}{63}$.

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
$0-2$	$1$
$2-4$	$3$
$4-6$	$5$
$6-8$	$3$
$8-10$	$1$

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

When a die is rolled $42$ times, it is observed that a face having the digit $i$ occurred $2i$ times. The mean deviation from the mean of this discrete frequency distribution is

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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 approximate value of the mean deviation about the mean for the following data is
Class Interval $0-2$ $2-4$ $4-6$ $6-8$ $8-10$
Frequency $1$ $2$ $3$ $2$ $1$

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