$stdDevPop (aggregation)

Result Type

$stdDevPop returns the population standard deviation of the input values as a decimal.

Non-numeric Values

$stdDevPop ignores non-numeric values. If all operands for a $stdDevPop are non-numeric, $stdDevPop returns null.

Single Value

If the sample consists of a single numeric value, $stdDevPop returns 0.

Array Operand

In the $group and $setWindowFields stages, if the expression resolves to an array, $stdDevPop treats the operand as a non-numerical value and has no effect on the calculation.

In the other supported stages:

• With a single expression as its operand, if the expression resolves to an array, $stdDevPop traverses into the array to operate on the numeric elements of the array to return a single value.

• With a list of expressions as its operand, if any of the expressions resolves to an array, $stdDevPop does not traverse into the array but instead treats the array as a non-numeric value.

Window Values

Behavior with values in a $setWindowFields stage window:

• Ignores non-numeric values, null values, and missing fields in a window.

• If the window is empty, returns null.

• If the window contains a NaN value, returns null.

• If the window contains Infinity values, returns null.

• If none of the previous points apply, returns a double value.

Use in $group Stage

Create a collection called users with the following documents:

db.users.insertMany( [
   { _id : 1, name : "dave123", quiz : 1, score : 85 },
   { _id : 2, name : "dave2", quiz : 1, score : 90 },
   { _id : 3, name : "ahn", quiz : 1, score : 71 },
   { _id : 4, name : "li", quiz : 2, score : 96 },
   { _id : 5, name : "annT", quiz : 2, score : 77 },
   { _id : 6, name : "ty", quiz : 2, score : 82 }
] )

The following example calculates the standard deviation of each quiz:

db.users.aggregate( [
   { $group: { _id: "$quiz", stdDev: { $stdDevPop: "$score" } } }
] )

The operation returns the following results:

{ "_id" : 2, "stdDev" : 8.04155872120988 }
{ "_id" : 1, "stdDev" : 8.04155872120988 }

Use in $project Stage

Create an example collection named quizzes with the following documents:

db.quizzes.insertMany( [
   {
      _id : 1,
      scores : [
         { name : "dave123", score : 85 },
         { name : "dave2", score : 90 },
         { name : "ahn", score : 71 }
      ]
   },
   {
      _id : 2,
      scores : [
         { name : "li", quiz : 2, score : 96 },
         { name : "annT", score : 77 },
         { name : "ty", score : 82 }
      ]
   }
] )

The following example calculates the standard deviation of each quiz:

db.quizzes.aggregate( [
   { $project: { stdDev: { $stdDevPop: "$scores.score" } } }
] )

The operation returns the following results:

{ _id : 1, stdDev : 8.04155872120988 }
{ _id : 2, stdDev : 8.04155872120988 }

Use in $setWindowFields Stage

Create a cakeSales collection that contains cake sales in the states of California (CA) and Washington (WA):

db.cakeSales.insertMany( [
   { _id: 0, type: "chocolate", orderDate: new Date("2020-05-18T14:10:30Z"),
     state: "CA", price: 13, quantity: 120 },
   { _id: 1, type: "chocolate", orderDate: new Date("2021-03-20T11:30:05Z"),
     state: "WA", price: 14, quantity: 140 },
   { _id: 2, type: "vanilla", orderDate: new Date("2021-01-11T06:31:15Z"),
     state: "CA", price: 12, quantity: 145 },
   { _id: 3, type: "vanilla", orderDate: new Date("2020-02-08T13:13:23Z"),
     state: "WA", price: 13, quantity: 104 },
   { _id: 4, type: "strawberry", orderDate: new Date("2019-05-18T16:09:01Z"),
     state: "CA", price: 41, quantity: 162 },
   { _id: 5, type: "strawberry", orderDate: new Date("2019-01-08T06:12:03Z"),
     state: "WA", price: 43, quantity: 134 }
] )

This example uses $stdDevPop in the $setWindowFields stage to output the population standard deviation of the cake sales quantity for each state:

db.cakeSales.aggregate( [
   {
      $setWindowFields: {
         partitionBy: "$state",
         sortBy: { orderDate: 1 },
         output: {
            stdDevPopQuantityForState: {
               $stdDevPop: "$quantity",
               window: {
                  documents: [ "unbounded", "current" ]
               }
            }
         }
      }
   }
] )

In the example:

• partitionBy: "$state" partitions the documents in the collection by state. There are partitions for CA and WA.

• sortBy: { orderDate: 1 } sorts the documents in each partition by orderDate in ascending order (1), so the earliest orderDate is first.

• output sets the stdDevPopQuantityForState field to the quantity population standard deviation value using $stdDevPop that is run in a documents window.

  The window contains documents between an unbounded lower limit and the current document in the output. This means $stdDevPop returns the quantity population standard deviation value for the documents between the beginning of the partition and the current document.

In this example output, the quantity population standard deviation value for CA and WA is shown in the stdDevPopQuantityForState field:

{ _id : 4, type : "strawberry", orderDate : ISODate("2019-05-18T16:09:01Z"),
  state : "CA", price : 41, quantity : 162, stdDevPopQuantityForState : 0 }
{ _id : 0, type : "chocolate", orderDate : ISODate("2020-05-18T14:10:30Z"),
  state : "CA", price : 13, quantity : 120, stdDevPopQuantityForState : 21 }
{ _id : 2, type : "vanilla", orderDate : ISODate("2021-01-11T06:31:15Z"),
  state : "CA", price : 12, quantity : 145, stdDevPopQuantityForState : 17.249798710580816 }
{ _id : 5, type : "strawberry", orderDate : ISODate("2019-01-08T06:12:03Z"),
  state : "WA", price : 43, quantity : 134, stdDevPopQuantityForState : 0 }
{ _id : 3, type : "vanilla", orderDate : ISODate("2020-02-08T13:13:23Z"),
  state : "WA", price : 13, quantity : 104, stdDevPopQuantityForState : 15 }
{ _id : 1, type : "chocolate", orderDate : ISODate("2021-03-20T11:30:05Z"),
  state : "WA", price : 14, quantity : 140, stdDevPopQuantityForState : 15.748015748023622 }