Calculate the median in MongoDB aggregation framework

Starting Mongo 4.4, the $group stage has a new aggregation operator $accumulator allowing custom accumulations of documents as they get grouped, via javascript user defined functions.

Thus, in order to find the median:

// { "a" : 25, "b" : 12 }
// { "a" : 89, "b" : 7  }
// { "a" : 25, "b" : 17 }
// { "a" : 25, "b" : 24 }
// { "a" : 89, "b" : 15 }
db.collection.aggregate([
  { $group: {
    _id: "$a",
    median: {
      $accumulator: {
        accumulateArgs: ["$b"],
        init: function() { return []; },
        accumulate: function(bs, b) { return bs.concat(b); },
        merge: function(bs1, bs2) { return bs1.concat(bs2); },
        finalize: function(bs) {
          bs.sort(function(a, b) { return a - b });
          var mid = bs.length / 2;
          return mid % 1 ? bs[mid - 0.5] : (bs[mid - 1] + bs[mid]) / 2;
        },
        lang: "js"
      }
    }
  }}
])
// { "_id" : 25, "median" : 17 }
// { "_id" : 89, "median" : 11 }

The accumulator:

• accumulates on the field b (accumulateArgs)
• is initialised to an empty array (init)
• accumulates b items in an array (accumulate and merge)
• and finally performs the median calculation on b items (finalize)

While maxiplay's answer is not accurate, it did lead me in the correct direction. The problem with the given solution is that it only works when the number of records is even. Because for odd number of records, one simply needs to take the value at midpoint without having to calculate an average.

This is how I got it to work.

db.collection.aggregate([
{ "$match": { "processingStatus": "Completed" } },
{ "$sort": { "value": 1 } },
{ 
    "$group": {
        "_id": "$userId",
        "valueArray": {
            "$push": "$value"
        }
    } 
},
{
    "$project": {
        "_id": 0,
        "userId": "$_id",
        "valueArray": 1,
        "size": { "$size": ["$valueArray"] }
    }
},
{
    "$project": {
        "userId": 1,
        "valueArray": 1,
        "isEvenLength": { "$eq": [{ "$mod": ["$size", 2] }, 0 ] },
        "middlePoint": { "$trunc": { "$divide": ["$size", 2] } }
    }
},
{
    "$project": {
        "userId": 1,
        "valueArray": 1,
        "isEvenLength": 1,
        "middlePoint": 1,
        "beginMiddle": { "$subtract": [ "$middlePoint", 1] },
        "endMiddle": "$middlePoint"
    }
},
{
    "$project": {
        "userId": 1,
        "valueArray": 1,
        "middlePoint": 1,
        "beginMiddle": 1,
        "beginValue": { "$arrayElemAt": ["$valueArray", "$beginMiddle"] },
        "endValue": { "$arrayElemAt": ["$valueArray", "$endMiddle"] },
        "isEvenLength": 1
    }
},
{
    "$project": {
        "userId": 1,
        "valueArray": 1,
        "middlePoint": 1,
        "beginMiddle": 1,
        "beginValue": 1,
        "endValue": 1,
        "middleSum": { "$add": ["$beginValue", "$endValue"] },
        "isEvenLength": 1
    }
},
{
    "$project": {
        "userId": 1,
        "valueArray": 1,
        "median": { 
            "$cond": { 
                if: "$isEvenLength", 
                then: { "$divide": ["$middleSum", 2] },
                else:  { "$arrayElemAt": ["$valueArray", "$middlePoint"] }
            } 
        }
    }
}
])