In a histogram, the areas of the rectangles a | vedclass

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(B) In a histogram, the area of each rectangle is given by the formula: $	ext{Area} = 	ext{Width} 	imes 	ext{Height}$.Here, the $	ext{Width}$ rep

Vedclass · Accepted Answer

No, it is only true when the class sizes are equal.

Vedclass · Answer

(B) In a histogram, the area of each rectangle is given by the formula: $	ext{Area} = 	ext{Width} 	imes 	ext{Height}$.Here, the $	ext{Width}$ represents the class size and the $	ext{Height}$ represents the frequency density.Since the $	ext{Area}$ is proportional to the frequency, we have $	ext{Frequency} \propto 	ext{Width} 	imes 	ext{Height}$.If the class sizes (widths) are equal, then $	ext{Width}$ is constant, which implies $	ext{Frequency} \propto 	ext{Height}$.However, if the class sizes are different, the height of the rectangle is adjusted to maintain the proportionality of the area to the frequency.Therefore, the lengths (heights) of the rectangles are proportional to the frequencies only when the class sizes are the same.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$5$	$7$	$12$	$9$	$13$	$5$

In a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?

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