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{"sheet":"説明","index":0,"n_rows":41,"n_cols":2,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["標本平均の分布と大数の法則"]
[]
["説明"]
["n個の標本平均の分布は、抽出回数 N が大きくなるにしたがって正規分布に近づいていくことが知られています。"]
["また n が大きくなればなるほど、分布は、1/√nで、平均に近づいていくことが知られています。"]
["これらのことについては、教科書でも触れており、感覚的には理解できます。"]
[]
["今回、新学習指導要領に変わり、確率分布、統計分野が、より前面に出されてきたと思われます。"]
["統計は苦手と感じるのは、感覚的な理解が不十分なことが原因ではないでしょうか。"]
[]
["実は私も統計分野は、ここ数年教えていません。理由は現在の勤務校では確率分布、統計分野は教えないで、"]
["他の分野を選択履修しているからです。このような学校は意外と多いのではないでしょうか"]
[]
["しかし、新学習指導要領になり、もはや確率分布や統計は避けては通れないものになりそうです。"]
["そこで、この分野において、教科書では説明が省いているような個所を、生徒に直接、目に見える形で"]
["具現化できればと思い、エクセルを用いてさまざまな事象をシュミレーションすることを考えました。"]
[]
["エクセルについては、難しいプログラミング技術は持っておりませんが、いろいろ調べながらコツコツ"]
["作成しました。新学習指導要領での授業の一助になればと思っています。"]
[]
["作成したエクセルファイルはホームページで公開し、発信、共有を図っていきたいと考えています。"]
[]
["ファイルの説明"]
[]
["水色","の部分は数式が入っているセルです。"]
["黄色","の部分は数値が変更できるセルです。"]
[]
["プログラミングの流れは、次のとおりです。"]
["１、まず３００個のデータを用意しました。"]
["２、ランダム関数を用いて、重複しないk個の数字をランダムに取り出します。"]
["これは非復元抽出のため、多少手間がかかります。"]
["３、２で取り出したk個の数字を用いて、VLOOKUP関数で、データをk個ランダムに抜き出します。"]
["４、このk個の標本平均を計算します。"]
["５、この試行をn回繰り返します。ただしnは１００の倍数で設定します。"]
["６、n回の試行の結果を度数分布表にします。"]
["７、度数分布表をグラフにします。グラフは１００回ずつ更新されます。"]
["８、クリアしない限り、結果は加算されます。"]
[]
["用意したデータは３００個ですが、個数を変えたり、数値をいろいろ変えてみると面白いと思います。"]
["抜き出すk個についても、kをいろいろ変えてみると、分布が広がったり、平均に近づいたりするのが"]
["観察できて、面白いです。"]

{"sheet":"法則","index":1,"n_rows":348,"n_cols":102,"rows_kept":348,"cut":false,"hidden":false,"merged":[[46,0,46,1],[0,0,0,5],[46,13,46,15],[43,6,43,11],[2,5,2,6],[46,3,46,4]]}
["標本平均の分布と大数の法則、中心極限定理"]
[]
[null,"抽出標本数",10,null,null,"抽出（試行）回数",null,100,null,"現在",100,"回目"]
[null,"標本",1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100]
[null,"抽出No",50,67,79,93,122,141,166,172,239,242]
[null,"抽出データ",{"$f":"IF(C5=\"\",\"\",VLOOKUP(C5,$A$49:$B$348,2,FALSE))","v":80},0,60,90,85,35,90,25,25,40,"","","","","","","","","","","","","","","","","","","","","","",{"$f":"IF(AI5=\"\",\"\",VLOOKUP(AI5,$A$49:$B$348,2,FALSE))","v":""},"","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","",{"$f":"IF(BO5=\"\",\"\",VLOOKUP(BO5,$A$49:$B$348,2,FALSE))","v":""},"","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","",{"$f":"IF(CU5=\"\",\"\",VLOOKUP(CU5,$A$49:$B$348,2,FALSE))","v":""},{"$f":"IF(CV5=\"\",\"\",VLOOKUP(CV5,$A$49:$B$348,2,FALSE))","v":""},{"$f":"IF(CW5=\"\",\"\",VLOOKUP(CW5,$A$49:$B$348,2,FALSE))","v":""},{"$f":"IF(CX5=\"\",\"\",VLOOKUP(CX5,$A$49:$B$348,2,FALSE))","v":""}]
[null,"標本平均",{"$f":"ROUND(AVERAGE(C6:CX6),1)","v":53}]
[null,"母集団の平均",{"$f":"AVERAGE(B49:B348)","v":63.85}]
[null,"標本平均の平均",64.554000000000002]
[null,"標本平均の標準偏差",9.5496117198553705]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"データはB列の9行目以降にありますが、これは自由に変えられます。"]
[null,"データを変えたとしても分布が正規分布に近づくことがわかります。"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,"度数分布作成欄"]
[null,null,null,null,null,null,"階級の幅",null,"度数チェック","総数","平均","標準偏差"]
[null,null,null,null,null,null,1,null,{"$f":"SUM(I49:I239)","v":100},{"$f":"SUM(J49:J148)","v":500},{"$f":"SUM(K49:K148)/$J$46","v":64.554000000000002},{"$f":"SQRT(SUM(L49:L148)/J46-(K46)^2)","v":9.5496117198553705}]
["母集団の格納場所",null,null,"データ抽出欄",null,null,null,null,null,null,null,null,null,"乱数生成欄"]
["No","点数",null,"回数","標本平均",null,"階級","階級値","度数","総度数","階級値*総度数","階級値の２乗*総度数",null,"乱数の範囲","1から",300]
[1,0,null,1,48,null,0,{"$f":"IF(G50>100,\"\",(G49+G50)/2)","v":0.5},{"$f":"COUNTIF($E$49:$E$148,\"<\"&G50)-COUNTIF($E$49:$E$148,\"<\"&G49)","v":0},0,{"$f":"H49*J49","v":0},{"$f":"H49^2*J49","v":0},null,"求めたい乱数の個数",null,{"$f":"C3","v":10}]
[2,5,null,2,61.5,null,{"$f":"G49+$G$46","v":1},{"$f":"IF(G51>100,\"\",(G50+G51)/2)","v":1.5},0,0,{"$f":"H50*J50","v":0},{"$f":"H50^2*J50","v":0}]
[3,10,null,3,58.5,null,2,2.5,0,0,0,0,null,"乱数発生","重複削除","取出し乱数",null,"小さい順に並べて、間をつめる"]
[4,15,null,4,54,null,3,3.5,0,0,0,0,null,{"$f":"INT(RAND()*($P$48))+1","v":118},{"$f":"N52","v":118},{"$f":"N52","v":118},null,50]
[5,20,null,5,88.5,null,4,4.5,0,0,0,0,null,42,{"$f":"IF(COUNTIF(N$52:N52,N53)=0,N53,\"\")","v":42},{"$f":"IF(COUNTIF(O$52:O52,\">0\")<$P$49,O53,\"\")","v":42},null,67]
[6,25,null,6,50.5,null,5,5.5,0,0,0,0,null,23,{"$f":"IF(COUNTIF(N$52:N53,N54)=0,N54,\"\")","v":23},{"$f":"IF(COUNTIF(O$52:O53,\">0\")<$P$49,O54,\"\")","v":23},null,79]
[7,30,null,7,61.5,null,6,6.5,0,0,0,0,null,269,{"$f":"IF(COUNTIF(N$52:N54,N55)=0,N55,\"\")","v":269},{"$f":"IF(COUNTIF(O$52:O54,\">0\")<$P$49,O55,\"\")","v":269},null,93]
[8,35,null,8,69,null,7,7.5,0,0,0,0,null,153,{"$f":"IF(COUNTIF(N$52:N55,N56)=0,N56,\"\")","v":153},{"$f":"IF(COUNTIF(O$52:O55,\">0\")<$P$49,O56,\"\")","v":153},null,122]
[9,40,null,9,65,null,8,8.5,0,0,0,0,null,196,{"$f":"IF(COUNTIF(N$52:N56,N57)=0,N57,\"\")","v":196},{"$f":"IF(COUNTIF(O$52:O56,\">0\")<$P$49,O57,\"\")","v":196},null,141]
[10,45,null,10,70.5,null,9,9.5,0,0,0,0,null,80,{"$f":"IF(COUNTIF(N$52:N57,N58)=0,N58,\"\")","v":80},{"$f":"IF(COUNTIF(O$52:O57,\">0\")<$P$49,O58,\"\")","v":80},null,166]
[11,50,null,11,65.5,null,10,10.5,0,0,0,0,null,192,{"$f":"IF(COUNTIF(N$52:N58,N59)=0,N59,\"\")","v":192},{"$f":"IF(COUNTIF(O$52:O58,\">0\")<$P$49,O59,\"\")","v":192},null,172]
[12,55,null,12,58,null,11,11.5,0,0,0,0,null,202,{"$f":"IF(COUNTIF(N$52:N59,N60)=0,N60,\"\")","v":202},{"$f":"IF(COUNTIF(O$52:O59,\">0\")<$P$49,O60,\"\")","v":202},null,239]
[13,60,null,13,58,null,12,12.5,0,0,0,0,null,18,{"$f":"IF(COUNTIF(N$52:N60,N61)=0,N61,\"\")","v":18},{"$f":"IF(COUNTIF(O$52:O60,\">0\")<$P$49,O61,\"\")","v":18},null,242]
[14,65,null,14,64.5,null,13,13.5,0,0,0,0,null,150,{"$f":"IF(COUNTIF(N$52:N61,N62)=0,N62,\"\")","v":150},{"$f":"IF(COUNTIF(O$52:O61,\">0\")<$P$49,O62,\"\")","v":""}]
[15,70,null,15,52.5,null,14,14.5,0,0,0,0,null,46,{"$f":"IF(COUNTIF(N$52:N62,N63)=0,N63,\"\")","v":46},{"$f":"IF(COUNTIF(O$52:O62,\">0\")<$P$49,O63,\"\")","v":""}]
[16,75,null,16,81,null,15,15.5,0,0,0,0,null,125,{"$f":"IF(COUNTIF(N$52:N63,N64)=0,N64,\"\")","v":125},{"$f":"IF(COUNTIF(O$52:O63,\">0\")<$P$49,O64,\"\")","v":""}]
[17,80,null,17,73,null,16,16.5,0,0,0,0,null,216,{"$f":"IF(COUNTIF(N$52:N64,N65)=0,N65,\"\")","v":216},{"$f":"IF(COUNTIF(O$52:O64,\">0\")<$P$49,O65,\"\")","v":""}]
[18,85,null,18,68.5,null,17,17.5,0,0,0,0,null,115,{"$f":"IF(COUNTIF(N$52:N65,N66)=0,N66,\"\")","v":115},{"$f":"IF(COUNTIF(O$52:O65,\">0\")<$P$49,O66,\"\")","v":""}]
[19,90,null,19,65.5,null,18,18.5,0,0,0,0,null,130,{"$f":"IF(COUNTIF(N$52:N66,N67)=0,N67,\"\")","v":130},{"$f":"IF(COUNTIF(O$52:O66,\">0\")<$P$49,O67,\"\")","v":""}]
[20,95,null,20,48,null,19,19.5,0,0,0,0,null,173,{"$f":"IF(COUNTIF(N$52:N67,N68)=0,N68,\"\")","v":173},{"$f":"IF(COUNTIF(O$52:O67,\">0\")<$P$49,O68,\"\")","v":""}]
[21,100,null,21,56.5,null,20,20.5,0,0,0,0,null,198,{"$f":"IF(COUNTIF(N$52:N68,N69)=0,N69,\"\")","v":198},{"$f":"IF(COUNTIF(O$52:O68,\">0\")<$P$49,O69,\"\")","v":""}]
[22,85,null,22,50,null,21,21.5,0,0,0,0,null,62,{"$f":"IF(COUNTIF(N$52:N69,N70)=0,N70,\"\")","v":62},{"$f":"IF(COUNTIF(O$52:O69,\">0\")<$P$49,O70,\"\")","v":""}]
[23,90,null,23,65,null,22,22.5,0,0,0,0,null,266,{"$f":"IF(COUNTIF(N$52:N70,N71)=0,N71,\"\")","v":266},{"$f":"IF(COUNTIF(O$52:O70,\">0\")<$P$49,O71,\"\")","v":""}]
[24,85,null,24,74,null,23,23.5,0,0,0,0,null,237,{"$f":"IF(COUNTIF(N$52:N71,N72)=0,N72,\"\")","v":237},{"$f":"IF(COUNTIF(O$52:O71,\">0\")<$P$49,O72,\"\")","v":""}]
[25,90,null,25,54.5,null,24,24.5,0,0,0,0,null,100,{"$f":"IF(COUNTIF(N$52:N72,N73)=0,N73,\"\")","v":100},{"$f":"IF(COUNTIF(O$52:O72,\">0\")<$P$49,O73,\"\")","v":""}]
[26,85,null,26,76,null,25,25.5,0,0,0,0,null,161,{"$f":"IF(COUNTIF(N$52:N73,N74)=0,N74,\"\")","v":161},{"$f":"IF(COUNTIF(O$52:O73,\">0\")<$P$49,O74,\"\")","v":""}]
[27,90,null,27,71.5,null,26,26.5,0,0,0,0,null,45,{"$f":"IF(COUNTIF(N$52:N74,N75)=0,N75,\"\")","v":45},{"$f":"IF(COUNTIF(O$52:O74,\">0\")<$P$49,O75,\"\")","v":""}]
[28,85,null,28,36,null,27,27.5,0,0,0,0,null,132,{"$f":"IF(COUNTIF(N$52:N75,N76)=0,N76,\"\")","v":132},{"$f":"IF(COUNTIF(O$52:O75,\">0\")<$P$49,O76,\"\")","v":""}]
[29,90,null,29,63.5,null,28,28.5,0,0,0,0,null,137,{"$f":"IF(COUNTIF(N$52:N76,N77)=0,N77,\"\")","v":137},{"$f":"IF(COUNTIF(O$52:O76,\">0\")<$P$49,O77,\"\")","v":""}]
[30,85,null,30,65.5,null,29,29.5,1,1,29.5,870.25,null,289,{"$f":"IF(COUNTIF(N$52:N77,N78)=0,N78,\"\")","v":289},{"$f":"IF(COUNTIF(O$52:O77,\">0\")<$P$49,O78,\"\")","v":""}]
[31,90,null,31,50.5,null,30,30.5,0,0,0,0,null,42,{"$f":"IF(COUNTIF(N$52:N78,N79)=0,N79,\"\")","v":""},{"$f":"IF(COUNTIF(O$52:O78,\">0\")<$P$49,O79,\"\")","v":""}]
[32,85,null,32,66,null,31,31.5,0,0,0,0,null,203,{"$f":"IF(COUNTIF(N$52:N79,N80)=0,N80,\"\")","v":203},{"$f":"IF(COUNTIF(O$52:O79,\">0\")<$P$49,O80,\"\")","v":""}]
[33,90,null,33,82,null,32,32.5,{"$f":"COUNTIF($E$49:$E$148,\"<\"&G82)-COUNTIF($E$49:$E$148,\"<\"&G81)","v":0},0,0,0,null,95,{"$f":"IF(COUNTIF(N$52:N80,N81)=0,N81,\"\")","v":95},{"$f":"IF(COUNTIF(O$52:O80,\">0\")<$P$49,O81,\"\")","v":""}]
[34,0,null,34,64,null,33,33.5,0,1,33.5,1122.25,null,235,{"$f":"IF(COUNTIF(N$52:N81,N82)=0,N82,\"\")","v":235},{"$f":"IF(COUNTIF(O$52:O81,\">0\")<$P$49,O82,\"\")","v":""}]
[35,5,null,35,80,null,34,34.5,0,1,34.5,1190.25,null,249,{"$f":"IF(COUNTIF(N$52:N82,N83)=0,N83,\"\")","v":249},{"$f":"IF(COUNTIF(O$52:O82,\">0\")<$P$49,O83,\"\")","v":""}]
[36,10,null,36,68,null,35,35.5,0,0,0,0,null,{"$f":"INT(RAND()*($P$48))+1","v":209},{"$f":"IF(COUNTIF(N$52:N83,N84)=0,N84,\"\")","v":209},{"$f":"IF(COUNTIF(O$52:O83,\">0\")<$P$49,O84,\"\")","v":""}]
[37,15,null,37,63,null,36,36.5,1,1,36.5,1332.25,null,159,{"$f":"IF(COUNTIF(N$52:N84,N85)=0,N85,\"\")","v":159},{"$f":"IF(COUNTIF(O$52:O84,\">0\")<$P$49,O85,\"\")","v":""}]
[38,20,null,38,78,null,37,37.5,0,0,0,0,null,46,{"$f":"IF(COUNTIF(N$52:N85,N86)=0,N86,\"\")","v":""},{"$f":"IF(COUNTIF(O$52:O85,\">0\")<$P$49,O86,\"\")","v":""}]
[39,25,null,39,52.5,null,38,38.5,0,0,0,0,null,142,{"$f":"IF(COUNTIF(N$52:N86,N87)=0,N87,\"\")","v":142},{"$f":"IF(COUNTIF(O$52:O86,\">0\")<$P$49,O87,\"\")","v":""}]
[40,30,null,40,57,null,39,39.5,0,0,0,0,null,90,{"$f":"IF(COUNTIF(N$52:N87,N88)=0,N88,\"\")","v":90},{"$f":"IF(COUNTIF(O$52:O87,\">0\")<$P$49,O88,\"\")","v":""}]
[41,35,null,41,77.5,null,40,40.5,0,0,0,0,null,250,{"$f":"IF(COUNTIF(N$52:N88,N89)=0,N89,\"\")","v":250},{"$f":"IF(COUNTIF(O$52:O88,\">0\")<$P$49,O89,\"\")","v":""}]
[42,40,null,42,61.5,null,41,41.5,1,1,41.5,1722.25,null,51,{"$f":"IF(COUNTIF(N$52:N89,N90)=0,N90,\"\")","v":51},{"$f":"IF(COUNTIF(O$52:O89,\">0\")<$P$49,O90,\"\")","v":""}]
[43,45,null,43,67,null,42,42.5,0,1,42.5,1806.25,null,3,{"$f":"IF(COUNTIF(N$52:N90,N91)=0,N91,\"\")","v":3},{"$f":"IF(COUNTIF(O$52:O90,\">0\")<$P$49,O91,\"\")","v":""}]
[44,50,null,44,71.5,null,43,43.5,0,1,43.5,1892.25,null,298,{"$f":"IF(COUNTIF(N$52:N91,N92)=0,N92,\"\")","v":298},{"$f":"IF(COUNTIF(O$52:O91,\">0\")<$P$49,O92,\"\")","v":""}]
[45,55,null,45,67.5,null,44,44.5,0,1,44.5,1980.25,null,102,{"$f":"IF(COUNTIF(N$52:N92,N93)=0,N93,\"\")","v":102},{"$f":"IF(COUNTIF(O$52:O92,\">0\")<$P$49,O93,\"\")","v":""}]
[46,60,null,46,57.5,null,45,45.5,0,6,273,12421.5,null,21,{"$f":"IF(COUNTIF(N$52:N93,N94)=0,N94,\"\")","v":21},{"$f":"IF(COUNTIF(O$52:O93,\">0\")<$P$49,O94,\"\")","v":""}]
[47,65,null,47,78,null,46,46.5,1,3,139.5,6486.75,null,49,{"$f":"IF(COUNTIF(N$52:N94,N95)=0,N95,\"\")","v":49},{"$f":"IF(COUNTIF(O$52:O94,\">0\")<$P$49,O95,\"\")","v":""}]
[48,70,null,48,70.5,null,47,47.5,0,2,95,4512.5,null,89,{"$f":"IF(COUNTIF(N$52:N95,N96)=0,N96,\"\")","v":89},{"$f":"IF(COUNTIF(O$52:O95,\">0\")<$P$49,O96,\"\")","v":""}]
[49,75,null,49,68.5,null,48,48.5,4,10,485,23522.5,null,183,{"$f":"IF(COUNTIF(N$52:N96,N97)=0,N97,\"\")","v":183},{"$f":"IF(COUNTIF(O$52:O96,\">0\")<$P$49,O97,\"\")","v":""}]
[50,80,null,50,78.5,null,49,49.5,0,10,495,24502.5,null,258,{"$f":"IF(COUNTIF(N$52:N97,N98)=0,N98,\"\")","v":258},{"$f":"IF(COUNTIF(O$52:O97,\">0\")<$P$49,O98,\"\")","v":""}]
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