[{"data":1,"prerenderedAt":179},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis\u002Fstandard-deviation-basics":3},{"topic":4,"category":146,"seo":150,"breadcrumbs":155,"prerequisites":162,"nextTopics":170,"relatedTopics":178},{"id":5,"slug":6,"title":7,"summary":8,"canonicalPath":9,"categoryPath":10,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"generatedAt":14,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":16,"expectedKnowledge":20,"learningGoal":23,"blocks":24},"high-school-mathematics-i-data-analysis-standard-deviation-basics","standard-deviation-basics","標準偏差","分散の平方根を標準偏差として求め、元データと同じ単位に戻して、平均からの散らばりを比較します。","\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis\u002Fstandard-deviation-basics","\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis","beginner","student_high",6,"2026-07-27","ai_generated",[17,18,7,19],"数学I","データの分析","分散",[19,21,22],"平方根","単位","分散から標準偏差を求め、同じ種類・単位のデータ間で散らばりの大小を説明できるようになる。",[25,30,39,56,62,79,85,95,105,111,127,136],{"id":26,"type":27,"title":7,"subtitle":28,"shortDefinition":29},"hero","HeroBlock","散らばりを元の単位へ戻す","分散は偏差を二乗するため、単位も二乗になります。その平方根を取った標準偏差なら、元データと同じ単位で散らばりを説明できます。",{"id":31,"type":32,"term":7,"definition":33,"plainExplanation":34,"keywords":35},"definition","DefinitionBlock","分散の正の平方根で、データの散らばりを元データと同じ単位で表す指標です。","得点データの分散が9点²なら、標準偏差は√9=3点です。0以上で、全ての値が同じなら0になります。同じテスト、同じ単位、同じ条件のデータ同士では、標準偏差が大きい方が平均の周りに広く散らばっています。",[36,37,38],"分散の平方根","元データと同じ単位","大きいほど広い散らばり",{"id":40,"type":41,"title":42,"formulas":43,"strategy":55},"formula","FormulaBlock","標準偏差の定義",[44],{"label":7,"expression":45,"meaning":46,"symbols":47,"tip":54},"standard_deviation = sqrt(variance)","分散の0以上の平方根を取る。",[48,51],{"symbol":49,"meaning":50},"σ","標準偏差を表す代表的な記号",{"symbol":52,"meaning":53},"σ²","分散を表す形","答えの単位を元データとそろえる。","分散→平方根→単位→文脈で比較、の順に読みます。",{"id":57,"type":58,"src":59,"alt":60,"caption":61},"diagram","DiagramBlock","\u002Fassets\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis\u002Fstandard-deviation-basics\u002Funit-restoration.svg","点の偏差を二乗して分散を作り平方根で標準偏差へ戻す流れの図","得点の偏差を二乗すると分散の単位は点²になります。最後に平方根を取る標準偏差では点へ戻るため、元の得点差と同じ尺度で二群の散らばりを比較できます。",{"id":63,"type":64,"columns":65,"rows":68,"summary":78},"compare","CompareBlock",[66,22,67],"指標","主な役割",[69,72,75],[19,70,71],"元の単位²","計算しやすく散らばりを保持",[7,73,74],"元の単位","元データの尺度で比較",[76,73,77],"平均","分布の中心を表す","中心と散らばりを別の指標で示し、単位も区別します。",{"id":80,"type":81,"scenario":82,"explanation":83,"result":84},"example","ExampleBlock","同じ平均60点のA組とB組で、分散が9点²と25点²だった。","A組の標準偏差は√9=3点、B組は√25=5点です。平均は同じでも、B組の得点は平均60点の周りにより広く散らばっていると説明できます。ただし標準偏差5点だから必ず全員が平均から5点以内、という意味ではありません。","中心は同じ60点、散らばりはB組の方が大きい、という二つの結論を分けます。",{"id":86,"type":87,"title":88,"points":89,"body":94},"reading-cue","KeyPointBlock","比較できる条件を先に確かめる",[90,91,92,93],"同じテストか","点数尺度が同じか","対象や期間が同じか","平均も併せて示す","数値の大小が意味をもつのは、同じ種類・単位・測定条件のデータを比べるときです。",{"id":96,"type":87,"title":97,"points":98,"body":104},"interpretation-boundary","標準偏差は個々の値の上限ではない",[99,100,101,102,103],"平均と標準偏差を組にして中心と散らばりを述べる","標準偏差が大きいほど平均からの広がりが大きい","同じ単位・同じ種類のデータ同士で比較する","極端な値があると標準偏差も影響を受ける","分布の偏りや外れ値の位置は図で補う","標準偏差3点は、すべての得点が平均から3点以内にあるという意味ではありません。分布全体の散らばりを一つの尺度で表す値なので、個々の得点を断定せず、箱ひげ図や元データの形も併せて読みます。",{"id":106,"type":107,"warningTitle":108,"message":109,"severity":106,"action":110},"warning","WarningBlock","大きいほど良い、ではない","標準偏差は散らばりの大きさであり、平均の高さや成績の良さを表しません。問いによって、ばらつきが小さいことの意味も変わります。","「何がどの周りにどれほど散らばるか」と文脈付きで書きましょう。",{"id":112,"type":113,"title":114,"questions":115},"quiz","QuizBlock","確認テスト",[116],{"question":117,"choices":118,"answerIndex":122,"choiceExplanations":123},"得点の分散が16点²のとき、標準偏差と単位はどれですか。",[119,120,121],"4点","16点","4点²",0,[124,125,126],"正解です。√16=4で、標準偏差は元データと同じ点の単位です。","16は分散の数値で、平方根を取っていません。","4は正しい数値ですが、標準偏差の単位は点²ではなく点です。",{"id":128,"type":129,"title":130,"points":131},"summary","SummaryBlock","まとめ",[132,133,134,135],"標準偏差は分散の平方根","0以上で元データと同じ単位","大きいほど平均の周りに広く散る","平均や測定条件と併せて読む",{"id":137,"type":138,"title":139,"nextTopics":140,"relatedKeywords":142},"next-action","NextActionBlock","分布の形と外れた値を図で見る",[141],"high-school-mathematics-i-data-analysis-box-plots-and-outliers",[143,144,145],"**箱ひげ図**","四分位範囲","外れ値",{"path":10,"title":18,"description":147,"parentPath":148,"accentToken":149},"分散、標準偏差、散布図、相関係数、仮説検定の考え方、外れ値を整理していくカテゴリです。","\u002Fhigh-school\u002Fmathematics-i","signal-blue",{"title":151,"description":152,"canonicalUrl":153,"ogImage":154},"標準偏差 | 数学I データの分析","分散の平方根としての標準偏差、単位、散らばりの比較を高校数学Iの範囲で学びます。","https:\u002F\u002Fzeqnilo.com\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis\u002Fstandard-deviation-basics","https:\u002F\u002Fzeqnilo.com\u002Fassets\u002Fsite\u002Fdefault-og.svg",[156,159,160,161],{"title":157,"path":158},"高校","\u002Fhigh-school",{"title":17,"path":148},{"title":18,"path":10},{"title":7,"path":9},[163],{"id":164,"title":165,"summary":166,"canonicalPath":167,"categoryPath":10,"categoryTitle":18,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":168},"high-school-mathematics-i-data-analysis-variance-basics","偏差と分散","各値が平均からどれだけ離れているかを偏差で表し、正負の相殺を二乗で防いで、その平均を分散として求めます。","\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis\u002Fvariance-basics",[17,18,169,19],"偏差",[171],{"id":141,"title":172,"summary":173,"canonicalPath":174,"categoryPath":10,"categoryTitle":18,"difficulty":11,"targetAudience":12,"estimatedMinutes":175,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":176},"箱ひげ図と外れ値","箱ひげ図で中央値と中央50%の広がりを比較し、離れた値を外れ値候補として原因確認してから扱います。","\u002Fhigh-school\u002Fmathematics-i\u002Fdata-analysis\u002Fbox-plots-and-outliers",5,[17,18,177,145],"箱ひげ図",[],1785565322079]