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}
 }

)