{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/weight-a-combined-average-by-what-it-represents",
  "id": "MHC-D-RESEARCH-0247",
  "version": "0.1.0",
  "title": "Weight a combined average by what it represents",
  "summary": "A tiny group does not acquire equal weight because its result occupies one spreadsheet cell.",
  "kind": "protocol",
  "body": "Recover each group's total from its mean and count, add the totals, then divide by the combined count. An average of group averages answers a different question unless equal group weighting is intentional.",
  "limits": [
    "Rounded group means produce an approximate combined mean; incompatible groups may not deserve pooling at all."
  ],
  "topics": [
    "union-numerical-reasoning"
  ],
  "intents": [],
  "source_ids": [
    "RS-AA03D333725959D7"
  ],
  "evidence": [
    {
      "claim": "The mean of combined groups is the sum of each group mean multiplied by its count, divided by the total count.",
      "source_id": "RS-AA03D333725959D7",
      "role": "supports",
      "note": "Groups must concern compatible observations and the counts must represent the intended weighting.",
      "locator": "Mean equals total divided by count; weighted-frequency expression"
    }
  ],
  "use_when": [
    "You need one average from groups of different sizes."
  ],
  "avoid_when": [
    "Rounded group means produce an approximate combined mean; incompatible groups may not deserve pooling at all."
  ],
  "example": "Ten cases averaging 10 minutes and ninety averaging 20 minutes give a combined mean of 19 minutes, not 15.",
  "check": "The weighting matches whether you mean the average case, person, group or period.",
  "steps": [
    "Check that the groups measure compatible observations.",
    "Multiply each mean by its corresponding count.",
    "Divide the sum of those products by the total count."
  ],
  "sources": [
    {
      "id": "RS-AA03D333725959D7",
      "title": "Introductory Statistics 2e, 2.5: Measures of the Center of the Data",
      "url": "https://openstax.org/books/introductory-statistics-2e/pages/2-5-measures-of-the-center-of-the-data"
    }
  ],
  "relations": [
    {
      "from": "MHC-D-RESEARCH-0247",
      "to": "MHC-D-RESEARCH-0248",
      "type": "useful_with",
      "url": "/knowledge/choose-the-average-that-fits-the-question"
    },
    {
      "from": "MHC-D-RESEARCH-0247",
      "to": "MHC-D-RESEARCH-0251",
      "type": "compare_with",
      "url": "/knowledge/build-an-overall-rate-from-totals"
    }
  ],
  "collections": [
    {
      "id": "RC-D976097B2A42D9AC",
      "title": "Make the numbers answer the right question",
      "url": "/collections/make-the-numbers-answer-the-right-question"
    }
  ]
}