MongoDB $stdDevPop Accumulator

Example 1 — Sample Data

Imagine six quiz results. Each document has a quiz number, a name, and a score.

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

How the Data Is Stored in MongoDB

After the insert, MongoDB keeps 6 documents in users. Run find() to see them:

db.users.find()

[
  { name: "dave123", quiz: 1, score: 85 },
  { name: "dave2", quiz: 1, score: 90 },
  { name: "ahn", quiz: 1, score: 71 },
  { name: "li", quiz: 2, score: 96 },
  { name: "annT", quiz: 2, score: 77 },
  { name: "ty", quiz: 2, score: 82 }
]

Read each document like this:

Quiz 1 scores: 85, 90, 71
Quiz 2 scores: 96, 77, 82

Next: $stdDevPop measures spread for the whole group.

How It Works

1. Insert once. The sample command adds 6 documents to users.
2. MongoDB stores fields as written. Each document keeps the same field names and values you inserted.
3. find() shows the same shape. What you inserted is what you get back—ready for $stdDevPop in the next examples.

Example 2 — Overall Population Spread

Goal: one standard deviation for every score in the collection. _id: null puts all documents in one group.

db.users.aggregate([
  {
    $group: {
      _id: null,
      stdDev: { $stdDevPop: "$score" },
      // handy to report alongside the spread
      avgScore: { $avg: "$score" }
    }
  }
]);

[
  {
    _id: null,
    stdDev: 8.180262108588081,
    avgScore: 83.5
  }
]

How It Works

1. One bucket. _id: null groups all six scores together.
2. Ignore non-numerics. Only numeric score values enter the calculation.
3. Population formula. MongoDB uses divide-by-N (not N−1) for $stdDevPop.
4. Mean for context. $avg in the same stage shows the center; $stdDevPop shows the spread.
5. Sample instead? Use $stdDevSamp when these scores are only a sample of a larger set.

Example 3 — Spread per Quiz

Goal: population standard deviation for each quiz separately. Both quizzes happen to share the same ≈ 8.0416 result with this sample.

db.users.aggregate([
  {
    $group: {
      _id: "$quiz",
      stdDev: { $stdDevPop: "$score" }
    }
  },
  { $sort: { _id: 1 } }
]);

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

How It Works

1. Split by quiz. _id: "$quiz" creates groups 1 and 2.
2. Three scores each. Quiz 1 uses 85, 90, 71; quiz 2 uses 96, 77, 82.
3. Same formula per bucket. Mean, squared diffs, divide by N, then square root.
4. Sort for reading. $sort orders quiz numbers ascending.
5. One value only? A quiz with a single numeric score would return 0.