{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/put-variation-beside-the-average",
  "id": "MHC-D-RESEARCH-0250",
  "version": "0.1.0",
  "title": "Put variation beside the average",
  "summary": "Five minutes on average can mean five minutes every time—or an unpleasant lottery.",
  "kind": "question",
  "body": "Look at the spread as well as the centre. Range reveals extremes; standard deviation summarizes dispersion around the mean; an interquartile range focuses on the middle half. Choose a description that makes the decision-relevant variability visible.",
  "limits": [
    "Do not apply normal-distribution coverage rules merely because a standard deviation has been calculated."
  ],
  "topics": [
    "union-numerical-reasoning"
  ],
  "intents": [],
  "source_ids": [
    "RS-092BD6D253CE697B"
  ],
  "evidence": [
    {
      "claim": "Range and standard deviation describe different aspects of variation, which a mean alone cannot identify.",
      "source_id": "RS-092BD6D253CE697B",
      "role": "supports",
      "note": "A spread measure does not by itself explain the source of variation or establish a normal distribution.",
      "locator": "Definitions of range and standard deviation"
    }
  ],
  "use_when": [
    "Two options share the same mean but may differ in reliability."
  ],
  "avoid_when": [
    "Do not apply normal-distribution coverage rules merely because a standard deviation has been calculated."
  ],
  "example": "Durations of 4, 5 and 6 minutes and durations of 0, 5 and 10 minutes both average 5, but offer different predictability.",
  "check": "The comparison includes variability relevant to the user's experience or operational risk.",
  "question": "How much do ordinary observations vary? · Are rare extremes important to the decision? · Would a distribution or quantile summary reveal what one spread number hides?",
  "sources": [
    {
      "id": "RS-092BD6D253CE697B",
      "title": "Introductory Statistics 2e, 2.7: Measures of the Spread of the Data",
      "url": "https://openstax.org/books/introductory-statistics-2e/pages/2-7-measures-of-the-spread-of-the-data"
    }
  ],
  "relations": [],
  "collections": [
    {
      "id": "RC-D976097B2A42D9AC",
      "title": "Make the numbers answer the right question",
      "url": "/collections/make-the-numbers-answer-the-right-question"
    }
  ]
}