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I cannot understand the computation in the below article : https://logological.org/girlfriend

(https://i.stack.imgur.com/ZM5wA.png)

The writer finds the number of girls aged 18 and above multiplying the number of girls in the bin "15-19" (39 560 000) by a fraction which I don't understand where it comes from.

My thought is that he uses the frequency density distribution n/Δx, where n is the frequency and Δx is the bin width. But how does he come up with the numerator and why add 1 on both numerator and denominator?is it because he wants to find frequency +1 year?

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The set of women aged 15 to 19 in 1998 contains women of 5 distinct ages: 15, 16, 17, 18, and 19. 5 is 19 - 15 + 1 (the absolute-value signs aren't necessary if we subtract with the larger end first) rather than just 19 - 15 because the range is inclusive of its endpoints (we're avoiding a fencepost error).

The numerator corresponds to the set of women aged 18 to 21 in 2000, or equivalently, the set of women aged 16 to 19 in 1998. We get 21 - 18 + 1 by the same logic as above.

The smaller set is a subset of the larger set, so by dividing the set sizes, we get the probability that a variable distributed uniformly in the bigger set will land in the smaller set.

The final quotient is 4/5. In short, this is the right answer because the smaller set has 4 ages and the bigger set has 5.

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