mysql - How to compute the standard deviation with a "number" column? -

i have table in mysql :

value    number_ads 1        3 2        1 3        1 3        1 4        1 

i compute standard deviation of column value, taking account value 1 example should counted 3 times.

the result should :

avg = 2.1429     std = 1.124858267715973 

i tried following request, don't have result:

select  sum(value * number_ads) / sum(number_ads) avg, sqrt((sum(pow(value, 2)) - pow(2.1429, 2))/sum(number_ads))  `test` 

calculate square root of variance. variance difference between mean of (squares of values) , square of mean i.e, sum(xx)/count(n) - meanmean.

select  sum(value * number_ads) / sum(number_ads) avg, sqrt((sum(pow(value ,2) * number_ads)/sum(number_ads)) - avg * avg) `test` 

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