mongodb mapreduce aggregation solution or merge into alternative

Below is the logic that I am trying to implement but I am finding it really difficult to figure out a way with MongoDB/ Node.js app

Data: country, state, val1

I need to compute mean and std. deviation using the below formula. I checked other stack overflow posts but the std dev formula that i am working is not the same:

for each row -> group by country, state
    mean = sum(val1)/count -> 
for each row ->
    deviation += Math.pow((val1 - mean), 2)
for each row -> group by country, state
    std dev = Math.sqrt(dev/ count)

the problem is with the way deviation needs to be computed. It looks like I need an aggregation for Mean before computing the deviation/ std dev through Map reduce which I dont find a way to compute. Could anyone suggest a way to do this?

If it is not possible, do we have a way to issue an update statement in mongodb similar to the below traditional merge query? I shall update the mean value for all the rows and would later invoke Mapreduce for the deviation/std dev.

merge into Tbl1 a using
  (select b.country, b.state, sum(b.val1)/count(b.val1) as mean
     from Tbl1 b
     group by b.country, b.state) c
on (a.country = c.country and 
    a.state = c.state)
when matched
then update
       set a.mean = c.mean

I am pretty new to the nosql and nodejs and it would be great if you guys could suggest a solution/ alternative.