Sum and Count

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There are many ways to do this in MongoDB.

count() is a cursor method that takes a query and returns a number equal to the amount of documents that matched the query.
$sum is an aggregation operator availible in the $group stage, that can be used to both sum values and count the number of documents.
mapReduce can produce a sum or a count during the results stage by using JavaScript.

.count()

db.world.count({"continent":"Africa"})

$sum

db.world.aggregate([

   {"$group":{
       "_id":"$continent",
       "sum of populations":{$sum:"$population"},
       "count of countries":{$sum:1}
   }}

])

Array.sum()

db.world.mapReduce(

   function(){emit(this.continent, this.population)},
   function(k,v){ return Array.sum(v) },
   {out:{inline:1}}

)