How to calculate a pooled standard deviation in SQL?

Question

I am collecting page load times and storing them in a SQL table. Every minute, I want to "roll up" those stats, storing the number of hits, the average load time, and the standard deviation of the load time.

After a while, I want to "roll up" those ten-minute intervals by hour, preserving total hits, average page load time, and "pooled" standard deviation.

Here is the critical part of a test script I cooked up:

select
-- Pooled standard deviation
case when sum(NumHits) = 1
then null -- stddev is undefined when sample size = 1
else
    sqrt(
        (
            sum(
                (NumHits - 1) * square(StdDev) + NumHits * square(cast(AvgLoadTime as int))
            ) - 
            sum(NumHits) * square(sum(cast(NumHits as int) * AvgLoadTime) / sum(NumHits))
        ) / -- numerator
        (
            sum(NumHits) - 1
        ) -- denominator
    ) 
end 'StdDev'

You can also see a SQL Fiddle of the entire test script.

The pooled standard deviation math is based on this equation from Wikipedia:

My questions are:

1. What is the best way to calculate pooled standard deviation in SQL?
2. Will it kill performance?

Update:

Added a case statement to handle cases where the sum of all sample sizes = 1. In that case, standard deviation is undefined.