What you are doing is using the standard method taught in introductory
classes for calculating the S.D. by hand.

The variance is (Sum(X^2f)-Sum(Xf)^2)/Sum(f))/(Sum(f)-1) and the S.D.
is sqrt(Var)

While it is excellent for use 'by hand,' working from first principles
is superior when used with a computer. Doing so also removes the need
for the Xf and X^2f columns.

Given the first 2 columns, the average, mu, is Sum(Xf)/Sum(f). You can
calculate this with with just the X and f columns.

To get the variance, use Sum((X-mu)^2*f)/(Sum(f)-1). As for the mean,
you can calculate this with just the X and f columns.

Suppose the X data are in B3:B10 and the f data in C3:C10.

Then the average, mu, in, say cell D16 is
=SUMPRODUCT(B3:B10,C3:C10)/SUM(C3:C10)

Of course, if you have the Xf column, it is also equal to Sum(Xf)/Sum
(f)

Now, the Variance, in, say, cell H16, is
=SUMPRODUCT((B3:B10-$D$16)^2,C3:C10)/(SUM(C3:C10)-1)

And, of course, the S.D. is =SQRT(H16)

--
Regards,

Tushar Mehta
www.tushar-mehta.com
Excel, PowerPoint, and VBA add-ins, tutorials
Custom MS Office productivity solutions

In article , !o!m!
N!OT! says...
From a histogram I collected the following data, I'm trying to figure out
how to calculate the standard deviation of hours driving. I can do it
outside of using the stdev formula, but if I try to use the formula I mess
up my results.

Mean hrs= number of subjects/total hours driving (200/1580) = 7.9
Standard Deviation for hours driving: Needs to equal 1.05 I can get that by
taking 12702(power1580,2)/200 which = 220
taking that sum (220) and making another calculation. sqrt(220/200-1)
Those combined net the standard deviation, but there has to be an easier
way.... Any help would be appreciated.

x f xf x2f
Hours of driving Number of Subjects Total Hours driving
3.5 2 7 24.5
4.5 2 9 40.5
5.5 4 22 121
6.5 22 143 929.5
7.5 64 480 3600
8.5 90 765 6502.5
9.5 14 133 1263.5
10.5 2 21 220.5

56 199 1580 12702