# Re: calculating age 1790-1820

> > I'm not arguing the answer, just asking for -- how did you get
> > there?
> >
> > For the numeric overachievers, I'm sure it's obvious; for the rest
> > of us, it's far less obvious and mathematical "proof" that shows
> > each step would be a useful thing to have.
> >
> > singhals
>
> Each of the census entries provides a lower bound (he was born *no
> earlier* than this) or an upper bound (he was born *no later* than
> this) or both. To clarify which information each entry provides,
> you can make a table listing the bounding years.
>
> lower | upper
> -------+-------
> | 1774 "born before 1774"
> 1755 | 1774 "born 1755-1774"
> | 1765 "born before 1765"
> | 1775 "born before 1775"
> 1760 | 1770 "born between 1760 and 1770"
> ---------------
>
> The interval you want is the smallest one you can make from these
> bounding values, the one that begins at the latest lower bound and
> ends at the earliest upper bound. The latest lower bound is 1760,
> and the earliest upper bound is 1765.
>
> To see why this works, you can draw a diagram that shows each census
> entry as an interval on a timeline.
>
> 1750 1775
> <---------+----+--------- "born before 1774"
> -----+----+--------- "born 1755-1774"
> <---------+----+ "born before 1765"
> <---------+----+---------- "born before 1775"
> +----+----- "born between 1760 and 1770"
>
> The interval where all of these lines overlap is where the birth
> year has to fall, assuming all the data are right.
>
> The left edge of the interval, the latest lower bound, is on the
> line that's the shortest on the left side (the bottom line here).
>
> The right edge of the interval, the earliest upper bound, is on the
> line that's the shortest on the right side (third from the top).
>
> -- Ernie http://home.comcast.net/~erniew
> Ernie Wright <erniew@xxxxxxxxxxx>

Thanks, Ernie. So far this comes closest to making sense.

Cheryl

.

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