{"query": "Describe — mean, variance, standard deviation", "count": 20, "results": [{"id": "card_stats_describe", "title": "Describe — mean, variance, standard deviation", "shelf": "codex", "surface": "secular", "snippet": "The first thing data tells you: the mean (the centre) and the standard deviation (the typical distance from it, sealed as 2 for a textbook sample). The ruler of spread. Rests on the instruments.", "authority_tier": "engine_derived", "source": "Narrow Highway — statistics", "readable": false, "generated": false}, {"id": "card_theory_power_laws", "title": "Power laws & heavy tails (Zipf, Pareto)", "shelf": "theories", "surface": "secular", "snippet": "Power laws & heavy tails (Zipf, Pareto) — an engine domain that can touch it: statistics. Calibration: seals — exponents, rank-frequency fits and tail probabilities compute. A distribution where P(x) ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_statistical_learning_theory__bias_variance__generali", "title": "Statistical learning theory (bias-variance, generalization)", "shelf": "theories", "surface": "secular", "snippet": "Statistical learning theory (bias-variance, generalization) — an engine domain that can touch it: statistics. Calibration: map-only — bounds are asymptotic and assumption-laden. Why fitting the data y", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_modern_portfolio_theory", "title": "Modern portfolio theory (Markowitz)", "shelf": "theories", "surface": "secular", "snippet": "Modern portfolio theory (Markowitz) — an engine domain that can touch it: finance. Calibration: seals — variance, correlation and frontier points compute. Markowitz (1952): risk should be judged for t", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_central_limit_theorem", "title": "Central limit theorem", "shelf": "theories", "surface": "secular", "snippet": "Central limit theorem — an engine domain that can touch it: statistics. Calibration: partial — sampling checks verify; the asymptotic claim is map-only. Add up many independent random quantities with ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_4718aea696c6", "title": "Ignatius to the Trallians IX", "shelf": "patristics", "surface": "witness", "snippet": "Stop your ears, therefore, when any one speaks to you at variance with Jesus Christ, who was descended from David, and was also of Mary; who was truly born, and did eat and drink. He was truly persecu", "authority_tier": "father", "source": "Ignatius to the Trallians (shorter recension; trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_041763374eca", "title": "Fokker–Planck & Liouville — probability flow in statistical mechanics", "shelf": "science", "surface": "secular", "snippet": "The stochastic instantiation of probability-as-fluid. Fokker–Planck sets the current\nJ = μρ − D∇ρ (drift + diffusion); its steady state is the Boltzmann distribution ρ ∝ e^(−U/kT),\nwhich makes the cur", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_business_statistics_2e_key_terms_57407930", "title": "Key Terms — Introductory Business Statistics 2e", "shelf": "mathematics", "surface": "secular", "snippet": "Key Terms\n\nAverage\na number that describes the central tendency of the data; there are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean.", "authority_tier": "reference", "source": "OpenStax: Introductory Business Statistics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_business_statistics_key_terms_0917e002", "title": "Key Terms — Introductory Business Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "Key Terms\n\nAverage\na number that describes the central tendency of the data; there are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean.", "authority_tier": "reference", "source": "OpenStax: Introductory Business Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_statistics_2e_introduction_67ff0f10", "title": "Introduction — Introductory Statistics 2e", "shelf": "mathematics", "surface": "secular", "snippet": "Figure\n2.1\n\nWhen you have large amounts of data, you will need to organize it in a way that makes sense. These ballots from an election are rolled together with similar ballots to keep them organized.", "authority_tier": "reference", "source": "OpenStax: Introductory Statistics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_statistics_introduction_9071ac54", "title": "Introduction — Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "Figure\n2.1\n\nWhen you have a large amount of data, you will need to organize it in a way that makes sense. These ballots from an election are rolled together with similar ballots to keep them organized", "authority_tier": "reference", "source": "OpenStax: Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_introductory_statistics_introduction_67ff0f10", "title": "Introduction — Introductory Statistics", "shelf": "mathematics", "surface": "secular", "snippet": "Figure\n2.1\n\nWhen you have large amounts of data, you will need to organize it in a way that makes sense. These ballots from an election are rolled together with similar ballots to keep them organized.", "authority_tier": "reference", "source": "OpenStax: Introductory Statistics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_etym_variance", "title": "variance", "shelf": "etymology", "surface": "secular", "snippet": "variance: etymology (Webster 1913) — n.: [L. variantia.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_openstax_principles_data_science_3_2_measures_of_variation_aa553f23", "title": "3.2 Measures of Variation — Principles of Data Science", "shelf": "reference", "surface": "secular", "snippet": "3.2\n\nMeasures of Variation\n\nLearning Outcomes\n\nBy the end of this section, you should be able to:\n\n3.2.1\nDefine and calculate the range, the variance, and the standard deviation for a dataset.\n\n3.2.2\n", "authority_tier": "reference", "source": "OpenStax: Principles of Data Science (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_calc_v_probability_variance", "title": "Variance", "shelf": "calculations", "surface": "secular", "snippet": "Variance — probability. Formula: Var = sum (x-mu)^2 p. Canonical FORM: accumulation (total = integral of a rate) — engine verifier probability.variance — the deterministic check the concordance runs. ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_seal_faf2e985d8948566647fad8a05d1b78ede4a2f570b7098806c46d65d8fbe7a4c", "title": "Receipt faf2e985d894… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error_at\": null,\n    \"gap_at\": null,\n    \"steps\": 1,\n    \"verdict\": \"HOLDS\"\n   },\n   \"gat", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_deefbb6da8f4197da8d8350981196a674bbdbd469bff74b2d011f8b9b0ed38da", "title": "Receipt deefbb6da8f4… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"statistics\",\n  \"dimensions\": [\n   \"authority_trust\",\n   \"conservation_balance\",\n   \"reasoning\",\n   \"time_sequence\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"det", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_bridge_theory_reliability_tolerance_stack_up__central_limit_theorem", "title": "Bridge: Reliability & tolerance stack-up (RSS)  ↔  Central limit theorem", "shelf": "bridges", "surface": "secular", "snippet": "Reliability & tolerance stack-up (RSS) and Central limit theorem are the same form in different domains. root-sum-square stacking IS the CLT in the shop: independent variances add, so an assembly's to", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_seal_a8d17b16b7d12e663e7a40bd91089941e2a4230a27f48acf5dd6e183a7cfccd3", "title": "Receipt a8d17b16b7d1… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_26b983cb4400f31a84656a2b1081bcfde2bd75223d8a4ac23668bb1937524373", "title": "Receipt 26b983cb4400… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_stats_describe"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}