{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/distinguish-variation-in-cases-from-uncertainty-in-a-mean",
  "id": "MHC-D-RESEARCH-0263",
  "version": "0.1.0",
  "title": "Distinguish variation in cases from uncertainty in a mean",
  "summary": "Customers can have wildly different experiences while the average is estimated very precisely.",
  "kind": "concept",
  "body": "Standard deviation describes variation among observations. Standard error describes uncertainty in an estimator such as a mean. They answer different questions. Ask which quantity the bars show before concluding that individual results are consistent or that the mean is uncertain.",
  "limits": [
    "The familiar standard-error formula for a mean assumes an appropriate independent-sample model."
  ],
  "topics": [
    "union-statistical-judgment"
  ],
  "intents": [],
  "source_ids": [
    "RS-CD81D61C5370E043"
  ],
  "evidence": [
    {
      "claim": "For an independent sample mean under the usual model, its estimated standard error is the sample standard deviation divided by the square root of the sample count.",
      "source_id": "RS-CD81D61C5370E043",
      "role": "supports",
      "note": "Correlated, weighted or complex samples do not automatically follow this formula.",
      "locator": "Confidence-limit formula"
    }
  ],
  "use_when": [
    "A chart or report labels an error bar without explaining what it measures."
  ],
  "avoid_when": [
    "The familiar standard-error formula for a mean assumes an appropriate independent-sample model."
  ],
  "example": "Thousands of widely varying delivery times can produce a narrow confidence interval for the mean without making any individual delivery predictable.",
  "check": "The explanation matches the kind of uncertainty actually displayed.",
  "sources": [
    {
      "id": "RS-CD81D61C5370E043",
      "title": "Confidence Limits for the Mean",
      "url": "https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm"
    }
  ],
  "relations": [
    {
      "from": "MHC-D-RESEARCH-0263",
      "to": "MHC-D-RESEARCH-0264",
      "type": "useful_with",
      "url": "/knowledge/read-a-confidence-interval-as-a-procedure-with-assumptions"
    }
  ],
  "collections": [
    {
      "id": "RC-D4FD0B28897E9517",
      "title": "Check what a study can actually tell you",
      "url": "/collections/check-what-a-study-can-actually-tell-you"
    }
  ]
}