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}
  }
)