{"id":1333,"date":"2026-01-26T19:01:05","date_gmt":"2026-01-26T09:01:05","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1333"},"modified":"2026-01-27T13:10:40","modified_gmt":"2026-01-27T03:10:40","slug":"year12-math-1-2-27","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1333","title":{"rendered":"Year12 MATH 2-4-1"},"content":{"rendered":"\n

In QLD Year 12 General Mathematics Unit 4 (Chance), relative frequency is defined as the experimental probability<\/strong> of an event occurring, calculated by dividing the number of times an event occurs by the total number of trials. It is used to estimate the likelihood of events, especially when theoretical probabilities are unknown or when analyzing real-world data, such as weather patterns or, in this unit, potentially in conjunction with and\/or events. <\/p>\n\n\n\n

Formula<\/strong><\/p>\n\n\n\n

Relative Frequency<\/mtext>=<\/mo>Number of times the event occurs<\/mtext>Total number of trials<\/mtext><\/mfrac><\/mrow>Relative Frequency equals the fraction with numerator Number of times the event occurs and denominator Total number of trials end-fraction<\/annotation><\/semantics><\/math>Relative <\/p>\n\n\n\n

Key Aspects of Relative Frequency<\/strong> <\/p>\n\n\n\n

    \n
  • Experimental Nature:<\/strong> Unlike theoretical probability, which tells us what should<\/em> happen, relative frequency tells us what actually<\/em> happened in an experiment.<\/li>\n\n\n\n
  • Data Representation:<\/strong> It can be expressed as a fraction, decimal, or percentage.<\/li>\n\n\n\n
  • Reliability:<\/strong> As the number of trials increases, the relative frequency tends to get closer to the theoretical probability.<\/li>\n\n\n\n
  • “And” \/ “Or” Events:<\/strong> It is applied to estimate the probability of compound events, such as calculating the relative frequency of two events occurring together (“and”) or either event occurring (“or”).<\/li>\n\n\n\n
  • Total Sum:<\/strong> The sum of all relative frequencies in an experiment is always 1. <\/li>\n<\/ul>\n\n\n\n

    Example<\/strong>
    If a die is rolled 100 times and a 6 appears 21 times, the relative frequency of rolling a 6 is:<\/p>\n\n\n\n

    21<\/mn>100<\/mn><\/mfrac>=<\/mo>0.21<\/mn>or<\/mtext>21<\/mn>%<\/mo><\/mrow>21 over 100 end-fraction equals 0.21 or 21 %<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

    Relation to Other Unit 4 Concepts<\/strong> <\/p>\n\n\n\n

      \n
    • Relative vs. Theoretical:<\/strong> While a fair die has a theoretical probability of 1<\/mn>\/<\/mo>6<\/mn><\/mrow>1 \/ 6<\/annotation><\/semantics><\/math> (\u2248<\/mo>0.167<\/mn><\/mrow>is approximately equal to 0.167<\/annotation><\/semantics><\/math>) for any number, the experimental relative frequency may differ.<\/li>\n\n\n\n
    • Expected Frequency:<\/strong> Relative frequency is used to estimate future outcomes, where the expected frequency is calculated as Probability<\/mtext>\u00d7<\/mo>Total Trials<\/mtext><\/mrow>Probability cross Total Trials<\/annotation><\/semantics><\/math>Probability\u00d7Total Trials.\u00a0<\/li>\n<\/ul>\n\n\n\n

      ****************************************************************************<\/p>\n\n\n\n

      QLD 12\u5e74\u751f\u4e00\u822c\u6570\u5b66\u30e6\u30cb\u30c3\u30c84\uff08\u78ba\u7387\uff09\u3067\u306f\u3001\u76f8\u5bfe\u983b\u5ea6\u306f\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u5b9f\u9a13\u7684\u78ba\u7387\u3068\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u4e8b\u8c61\u306e\u767a\u751f\u56de\u6570\u3092\u7dcf\u8a66\u884c\u56de\u6570\u3067\u5272\u308b\u3053\u3068\u3067\u7b97\u51fa\u3055\u308c\u307e\u3059\u3002\u76f8\u5bfe\u983b\u5ea6\u306f\u3001\u7279\u306b\u7406\u8ad6\u7684\u306a\u78ba\u7387\u304c\u4e0d\u660e\u306a\u5834\u5408\u3084\u3001\u6c17\u8c61\u30d1\u30bf\u30fc\u30f3\u306a\u3069\u306e\u5b9f\u4e16\u754c\u306e\u30c7\u30fc\u30bf\u3092\u5206\u6790\u3059\u308b\u5834\u5408\u3001\u3042\u308b\u3044\u306f\u3053\u306e\u30e6\u30cb\u30c3\u30c8\u3067\u306fand\/or\u4e8b\u8c61\u3068\u95a2\u9023\u3057\u3066\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u53ef\u80fd\u6027\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u7528\u3044\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

      \u8a08\u7b97\u5f0f
      (\u76f8\u5bfe\u983b\u5ea6<\/mtext>=<\/mo>\u4e8b\u8c61\u306e\u767a\u751f\u56de\u6570<\/mtext>\u7dcf\u8a66\u884c\u56de\u6570<\/mtext><\/mfrac><\/mrow>\\text{\u76f8\u5bfe\u983b\u5ea6}=\\frac{\\text{\u4e8b\u8c61\u306e\u767a\u751f\u56de\u6570}}{\\text{\u7dcf\u8a66\u884c\u56de\u6570}}<\/annotation><\/semantics><\/math>)<\/p>\n\n\n\n

      \u76f8\u5bfe\u983b\u5ea6\u306e\u4e3b\u306a\u5074\u9762<\/p>\n\n\n\n

      \u5b9f\u9a13\u7684\u6027\u8cea\uff1a\u4f55\u304c\u8d77\u3053\u308b\u3079\u304d\u304b\u3092\u793a\u3059\u7406\u8ad6\u7684\u306a\u78ba\u7387\u3068\u306f\u7570\u306a\u308a\u3001\u76f8\u5bfe\u983b\u5ea6\u306f\u5b9f\u9a13\u3067\u5b9f\u969b\u306b\u4f55\u304c\u8d77\u3053\u3063\u305f\u304b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

      \u30c7\u30fc\u30bf\u306e\u8868\u73fe\uff1a\u5206\u6570\u3001\u5c0f\u6570\u3001\u307e\u305f\u306f\u30d1\u30fc\u30bb\u30f3\u30c6\u30fc\u30b8\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

      \u4fe1\u983c\u6027\uff1a\u8a66\u884c\u56de\u6570\u304c\u5897\u3048\u308b\u306b\u3064\u308c\u3066\u3001\u76f8\u5bfe\u983b\u5ea6\u306f\u7406\u8ad6\u7684\u306a\u78ba\u7387\u306b\u8fd1\u3065\u304f\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

      \u300c\u304b\u3064\u300d\uff0f\u300c\u307e\u305f\u306f\u300d\u4e8b\u8c61\uff1a\u8907\u5408\u4e8b\u8c61\u306e\u78ba\u7387\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u30012\u3064\u306e\u4e8b\u8c61\u304c\u540c\u6642\u306b\u767a\u751f\u3059\u308b\uff08\u300c\u304b\u3064\u300d\uff09\u5834\u5408\u306e\u76f8\u5bfe\u983b\u5ea6\u3001\u307e\u305f\u306f\u3069\u3061\u3089\u304b\u4e00\u65b9\u306e\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\uff08\u300c\u307e\u305f\u306f\u300d\uff09\u5834\u5408\u306e\u76f8\u5bfe\u983b\u5ea6\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

      \u7dcf\u548c\uff1a\u5b9f\u9a13\u306b\u304a\u3051\u308b\u3059\u3079\u3066\u306e\u76f8\u5bfe\u983b\u5ea6\u306e\u5408\u8a08\u306f\u5e38\u306b1\u3067\u3059\u3002<\/p>\n\n\n\n

      \u4f8b\uff1a\u30b5\u30a4\u30b3\u30ed\u3092100\u56de\u632f\u3063\u30666\u304c21\u56de\u51fa\u305f\u5834\u5408\u30016\u304c\u51fa\u308b\u76f8\u5bfe\u983b\u5ea6\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

      (21<\/mn>100<\/mn><\/mfrac>=<\/mo>0.21<\/mn> or <\/mtext>21<\/mn>%<\/mi><\/mrow>\\frac{21}{100}=0.21\\text{\\ or\\ }21\\%<\/annotation><\/semantics><\/math>)<\/p>\n\n\n\n

      \u30e6\u30cb\u30c3\u30c84\u306e\u4ed6\u306e\u6982\u5ff5\u3068\u306e\u95a2\u4fc2<\/p>\n\n\n\n

      \u76f8\u5bfe\u7684 vs. \u7406\u8ad6\u7684\u306a\u78ba\u7387\uff1a\u516c\u5e73\u306a\u30b5\u30a4\u30b3\u30ed\u306e\u7406\u8ad6\u7684\u306a\u78ba\u7387\u306f\u3001\u3069\u306e\u76ee\u306b\u5bfe\u3057\u3066\u3082(1\/6) (\u2248<\/mo>0.167<\/mn><\/mrow>\\approx 0.167<\/annotation><\/semantics><\/math>) \u3067\u3059\u304c\u3001\u5b9f\u9a13\u7684\u306a\u76f8\u5bfe\u983b\u5ea6\u306f\u7570\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

      \u4e88\u60f3\u983b\u5ea6: \u76f8\u5bfe\u983b\u5ea6\u306f\u5c06\u6765\u306e\u7d50\u679c\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4e88\u60f3\u983b\u5ea6\u306f (\u78ba\u7387<\/mtext>\u00d7<\/mo>\u5408\u8a08<\/mtext>\\\u8a66<\/mtext>\u884c\u56de\u6570<\/mtext><\/mrow><\/mrow>\\text{\u78ba\u7387}\\times \\text{\u5408\u8a08\\\u8a66\u884c\u56de\u6570}<\/annotation><\/semantics><\/math>) \u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n

      <\/p>\n","protected":false},"excerpt":{"rendered":"

      In QLD Year 12 General Mathematics Unit 4 (Chance), relative frequency is defined as the experimental probability of an event occurring, calculated by dividing the number of times an event occurs by the total number of trials. It is used to estimate the likelihood of events, especially when theoretical probabilities are unknown or when analyzing […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1333","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1333","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1333"}],"version-history":[{"count":3,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1333\/revisions"}],"predecessor-version":[{"id":1370,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1333\/revisions\/1370"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}