count = db.coll.count();
db.coll.find().sort( {"a":1} ).skip(count / 2 - 1).limit(1);

GroupOperation countByBookOwner = group("owner").count().as("nbBooks");

    SortOperation sortByCount = sort(Direction.ASC, "nbBooks");

    GroupOperation putInArray = group().push("nbBooks").as("nbBooksArray");

    ProjectionOperation getSizeOfArray = project("nbBooksArray").and("nbBooksArray").size().as("size");

    ProjectionOperation divideSizeByTwo = project("nbBooksArray").and("size").divide(2).as("middleFloat");

    ProjectionOperation getIntValueOfDivisionForBornLeft = project("middleFloat", "nbBooksArray").and("middleFloat")
            .project("trunc").as("beginMiddle");

    ProjectionOperation add1ToBornLeftToGetBornRight = project("beginMiddle", "middleFloat", "nbBooksArray")
            .and("beginMiddle").project("add", 1).as("endMiddle");

    ProjectionOperation arrayElementAt = project("beginMiddle", "endMiddle", "middleFloat", "nbBooksArray")
            .and("nbBooksArray").project("arrayElemAt", "$beginMiddle").as("beginValue").and("nbBooksArray")
            .project("arrayElemAt", "$endMiddle").as("endValue");

    ProjectionOperation averageForMedian = project("beginMiddle", "endMiddle", "middleFloat", "nbBooksArray",
            "beginValue", "endValue").and("beginValue").project("avg", "$endValue").as("median");

    Aggregation aggregation = newAggregation(countByBookOwner, sortByCount, putInArray, getSizeOfArray,
            divideSizeByTwo, getIntValueOfDivisionForBornLeft, add1ToBornLeftToGetBornRight, arrayElementAt,
            averageForMedian);

    long time = System.currentTimeMillis();
    AggregationResults<MedianContainer> groupResults = mongoTemplate.aggregate(aggregation, "book",
            MedianContainer.class);

{
"aggregate": "book" ,
"pipeline": [
    {
        "$group": {
            "_id": "$owner" ,
            "nbBooks": {
                "$sum": 1
            }
        }
    } , {
        "$sort": {
            "nbBooks": 1
        }
    } , {
        "$group": {
            "_id": null  ,
            "nbBooksArray": {
                "$push": "$nbBooks"
            }
        }
    } , {
        "$project": {
            "nbBooksArray": 1 ,
            "size": {
                "$size": ["$nbBooksArray"]
            }
        }
    } , {
        "$project": {
            "nbBooksArray": 1 ,
            "middleFloat": {
                "$divide": ["$size" , 2]
            }
        }
    } , {
        "$project": {
            "middleFloat": 1 ,
            "nbBooksArray": 1 ,
            "beginMiddle": {
                "$trunc": ["$middleFloat"]
            }
        }
    } , {
        "$project": {
            "beginMiddle": 1 ,
            "middleFloat": 1 ,
            "nbBooksArray": 1 ,
            "endMiddle": {
                "$add": ["$beginMiddle" , 1]
            }
        }
    } , {
        "$project": {
            "beginMiddle": 1 ,
            "endMiddle": 1 ,
            "middleFloat": 1 ,
            "nbBooksArray": 1 ,
            "beginValue": {
                "$arrayElemAt": ["$nbBooksArray" , "$beginMiddle"]
            } ,
            "endValue": {
                "$arrayElemAt": ["$nbBooksArray" , "$endMiddle"]
            }
        }
    } , {
        "$project": {
            "beginMiddle": 1 ,
            "endMiddle": 1 ,
            "middleFloat": 1 ,
            "nbBooksArray": 1 ,
            "beginValue": 1 ,
            "endValue": 1 ,
            "median": {
                "$avg": ["$beginValue" , "$endValue"]
            }
        }
    }
]

db.collection.aggregate([
{ "$match": { "processingStatus": "Completed" } },
{
    "$group": {
        "_id": "$userId",
        "valueArray": {
            "$push": "$value"
        }
    }
},
{ "$sort": { "value": 1 } },
{
    "$project": {
        "_id": 0,
        "userId": "$_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": { "$arrayElemAt": ["$stepsArray", "$beginMiddle"] },
        "endValue": { "$arrayElemAt": ["$stepsArray", "$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": ["$stepsArray", "$middlePoint"] }
            }
        }
    }
}
])