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#### Guest

i was reviewing my preset worksheet with the standard deviation function and

noticed that the out put result contains error.

Formula "=STDEV(K12:K111)" was set to to calculate standard deviation

between 0-100 sets of values in the column, where values can be whole numbers

or fractions, in respective columns. Formula was observed performing

perfectly with whole numbers, however, with fractions (or numbers with

decimal places), the output is invalid (in some sense).

You may test, with 60 sets of values "1" in a column, the STDEV is "0".

However, when applying the same formula to a fraction value "0.05", 60 sets

in a column, the STDEV is "4.9E-17". This is definitely a NO NO answer in

mathematics point of view. If you breakdown the calculation steps of a STDEV

formula "s2 = (âˆ‘(x-m)^2)/N" into multiple columns, it would be identified

that the culprit lies on the "âˆ‘(X-M)^2" formula, where x is the individual

value and m is the mean.

Example below demonstrates the breakdown of the column calculations:

x m N âˆ‘(x-m)2 s2 s

0.05 0.05 1 0 0 0

0.05 0.05 2 0 0 0

0.05 0.05 3 1.44E-34 4.81E-35 6.94E-18

0.05 0.05 4 0 0 0

0.05 0.05 5 0 0 0

0.05 0.05 6 2.89E-34 4.81E-35 6.94E-18

0.05 0.05 7 3.37E-34 4.81E-35 6.94E-18

:

:

0.05 0.05 58 1.01E-31 1.73E-33 4.16E-17

0.05 0.05 59 1.02E-31 1.73E-33 4.16E-17

0.05 0.05 60 1.42E-31 2.36E-33 4.86E-17

*Note that the âˆ‘(x-m)2 is calculated using array formula

"{=SUM(($A$2:A61-B61)^2)}", since mean is constantly changing.

Is this due to limitation of the excel formula (STDEV only works for whole

numbers)? Or is there any patch for this error?