Statement (I): The range of the ungrouped dat | vedclass

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Question

(A) Statement $(I)$: The range is defined as the difference between the maximum and minimum observations. Since intermediate observations do not affec

Vedclass · Accepted Answer

Statements $I$ and $II$ are true but statement $III$ is false

Vedclass · Answer

(A) Statement $(I)$: The range is defined as the difference between the maximum and minimum observations. Since intermediate observations do not affect the maximum or minimum values,the range remains unchanged. Thus,Statement $(I)$ is true.Statement $(II)$: $A$ well-known property of mean deviation is that it is minimized when calculated about the median. Thus,Statement $(II)$ is true.Statement $(III)$: For grouped data,the range is defined as the difference between the upper limit of the largest class and the lower limit of the smallest class. The statement provided swaps these,making it false.Therefore,Statements $I$ and $II$ are true but statement $III$ is false.

$x$	$1, 3, 5, 7, 9$
$f$	$4, 24, 28, 16, 8$

$x_i$	$2$	$4$	$6$	$8$	$10$	$12$	$14$	$16$
$f_i$	$4$	$4$	$\alpha$	$15$	$8$	$\beta$	$4$	$5$

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