MongoDB $stdDevSamp Accumulator

Example 1 — Sample Data

Imagine six quiz results treated as a sample of a larger class. 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: $stdDevSamp measures sample standard deviation.

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 $stdDevSamp in the next examples.

Example 2 — Overall Sample Spread

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

db.users.aggregate([
  {
    $group: {
      _id: null,
      stdDev: { $stdDevSamp: "$score" },
      avgScore: { $avg: "$score" }
    }
  }
]);

[
  {
    _id: null,
    stdDev: 8.96102672688794,
    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. Sample formula. MongoDB uses divide-by-(N−1) for $stdDevSamp.
4. Larger than population. With the same scores, sample stddev is larger than $stdDevPop (~8.18) because N−1 shrinks the denominator.
5. Mean for context. $avg shows the center; $stdDevSamp shows estimated spread.

Example 3 — Sample Spread per Quiz

Goal: sample standard deviation for each quiz separately. Both quizzes share the same ≈ 9.8489 result with this sample.

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

[
  { _id: 1, stdDev: 9.848857801796104 },
  { _id: 2, stdDev: 9.848857801796104 }
]

How It Works

1. Split by quiz. _id: "$quiz" creates groups 1 and 2.
2. Three scores each. Enough for N−1 (denominator 2).
3. Sample variance. Quiz 1: 194 / 2 = 97, then √97 ≈ 9.8489.
4. Sort for reading. $sort orders quiz numbers ascending.
5. One value only? A quiz with a single numeric score would return null.