# [Maths-Education] SUM(.) etc. with intervals rather than point-estimates

**John Bibby, QED/MatheMagic (York, England), maths popularisers**
qed@enterprise.net

*Sun, 22 Oct 2000 19:18:43 +0100*

Does anybody know how best I can set up e.g. a function in e.g. Excel so
that I can easily SUM a set of numbers, where the user has the option of
putting in an interval estimate.
e.g. (2,4) could represent a 90% probability interval with 2 and 4 as
end-points i.e. 3+-1 (+- menas "+ or -")
(2,4) could then be added to (6,10)
and the answer would be as follows:
(2,4) means 3 +-1
(6,10) means 8+-2
The sum is 11 +- sqrt(1**2 + 2**2) = 11 +-sqrt(5) = 11+-2.24 = (8.76, 13.24)
Thus (2,4) + (6,10) = (8.76, 13.24)
I want a function that will do the above or similar for any number of
arguments - and if it could do other calculations on intervals that would be
very nice too!
This wd be useful in e.g. financial spreadsheets where items have different
amounts of uncertainty. (It can of course be done by doubling the number of
cells, but I want something whcih can be used easily by lay practitioners.)
Please reply to qed@enterprise.net
Thanks
JOHN BIBBY