{"id":790,"date":"2024-03-21T13:19:37","date_gmt":"2024-03-21T04:19:37","guid":{"rendered":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=790"},"modified":"2024-06-03T09:14:39","modified_gmt":"2024-06-03T00:14:39","slug":"top-math2-1q-2h-1","status":"publish","type":"post","link":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=790","title":{"rendered":"\u6570\u5b66II_1Q2H_1"},"content":{"rendered":"\n\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u518d\u751f\u30ea\u30b9\u30c8<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
\u30c6\u30ad\u30b9\u30c8<\/span><\/td>\n\u6f14\u7fd2<\/span><\/td>\n\u6f14\u7fd2\u89e3\u7b54<\/span><\/td>\n\u8ab2\u984c<\/span><\/td>\n\u89e3\u8aac<\/span><\/td>\n<\/tr>\n
1Q2H_1<\/span><\/a><\/td>\n1Q2H_E1<\/span><\/a><\/td>\n1Q2H_ES1<\/span><\/a><\/td>\n1Q2H_K1<\/span><\/a><\/td>\n1Q2H_V1<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u30c7\u30fc\u30bf\uff5b$ 1,2,2,2,4,4,5,5 $\uff5d\u306b\u3064\u3044\u3066\u3001\uff15\u6570\u8981\u7d04$=?$\u3001 \u7bb1\u30d2\u30b2\u56f3$=?$ <\/div>
\u6700\u5c0f\u5024 Min$=1$<\/span>\u3001\u6700\u5927\u5024 Max$=5$<\/span>
\u30c7\u30fc\u30bf\u6570 $8$ \u3088\u308a\u30014\u756a\u76ee\u30685\u756a\u76ee\u306e\u9593\u304c\u771f\u3093\u4e2d<\/span>\u306a\u306e\u3067\u3001
\u4e2d\u592e\u5024$\\; Q_2=$\u300c4\u756a\u76ee\u30685\u756a\u76ee\u306e\u5e73\u5747\u300d<\/span>$ =\\dfrac{2+4}{2}=3$
\u7b2c\uff11\u56db\u5206\u4f4d\u6570$\\;Q_1\uff1d$\u300c\u524d\u534a\u306e\u4e2d\u592e\u5024\u300d<\/span>$=\\dfrac{2+2}{2}=2$
\u7b2c3\u56db\u5206\u4f4d\u6570$\\;Q_3\uff1d$\u300c\u5f8c\u534a\u306e\u4e2d\u592e\u5024\u300d<\/span>$=\\dfrac{4+5}{2}=4.5$
\u56db\u5206\u4f4d\u7bc4\u56f2 IQR<\/span>$=Q_3-Q_1=4.5-2=2.5$
$+$<\/span>$=\\mu=$\u5e73\u5747$=\\dfrac{1+2+2+2+4+4+5+5}{8}=\\dfrac{25}{8}=3.125$\"\"<\/div><\/div>
<\/span>Targets<\/div>
\uff11.\u30c7\u30fc\u30bf\u304b\u3089\u6700\u983b\u5024<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\uff12. \uff15\u6570\u8981\u7d04(\u6700\u5927\u30fb\u6700\u5c0f\u30fb\u4e2d\u592e\u5024\u30fb\u7b2c\uff11\u30fb\u7b2c\uff13\u56db\u5206\u4f4d\u6570<\/span>)\u304c\u6c42\u3081\u3089\u308c\u308b
\uff13. \u5e73\u5747<\/span>\u3068IQR<\/span>=\u56db\u5206\u4f4d\u7bc4\u56f2\u3082\u6c42\u3081\u3066\u3001\u7bb1\u30d2\u30b2\u56f3<\/span>\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b<\/div><\/div> <\/div>\n
\n\n\n\n\n\n
1Q2H_2<\/span><\/a><\/td>\n1Q2H_E2<\/span><\/a><\/td>\n1Q2H_ES2<\/span><\/a><\/td>\n1Q2H_K2<\/span><\/a><\/td>\n1Q2H_V2<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u30c7\u30fc\u30bf\uff5b$ 1,2,2,3,3,4,4,5 $\uff5d\u306b\u3064\u3044\u3066\u3001\u5e73\u5747\u30fb\u5206\u6563\u30fb\u6a19\u6e96\u504f\u5dee$=?$\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0$=?$ <\/div>
\uff11\u304c\uff11\u500b\u3001\uff12\u304c\uff12\u500b\u3001\uff13\u304c\uff12\u500b\u3001\uff14\u304c\uff12\u500b\u3001\uff15\u304c\uff11\u500b\u2192\u5ea6\u6570\u5206\u5e03\u8868<\/p>\n\n\n\n\n\n
$x$<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n$\\Sigma$\u8a08<\/td>\n<\/tr>\n
$f$<\/td>\n1<\/td>\n2<\/td>\n2<\/td>\n2<\/td>\n1<\/td>\n$n=8$<\/td>\n<\/tr>\n
$xf$<\/td>\n1<\/td>\n4<\/td>\n6<\/td>\n8<\/td>\n5<\/td>\n$\\Sigma xf=24$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5e73\u5747\u3000<\/span>$\\mu=\\dfrac{1}{n} \\Sigma xf=\\dfrac{1}{8} \\cdot 24=3$<\/p>\n\n\n\n\n\n
$(x-\\mu)^2$<\/td>\n4<\/td>\n1<\/td>\n0<\/td>\n1<\/td>\n4<\/td>\n$\\Sigma$\u8a08<\/td>\n<\/tr>\n
$f$<\/td>\n1<\/td>\n2<\/td>\n2<\/td>\n2<\/td>\n1<\/td>\n$n=8$<\/td>\n<\/tr>\n
$(x-\\mu)^2f$<\/td>\n4<\/td>\n2<\/td>\n0<\/td>\n2<\/td>\n4<\/td>\n$\\Sigma(x-\\mu)^2f=12$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5206\u6563\u3000<\/span>$\\sigma^2=\\dfrac{1}{n} \\Sigma (x-\\mu)^2f=\\dfrac{1}{8} \\cdot 12=\\dfrac{3}{2}=1.5$
\u6a19\u6e96\u504f\u5dee\u3000<\/span>$\\sigma=\\sqrt{\\dfrac{3}{2}}=\\dfrac{\\sqrt{6}}{2}$\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u5ea6\u6570\u6298\u7dda<\/span>\u2192\u00a0\"\"<\/p>\n<\/div><\/div>

<\/span>Targets<\/div>
1. \u30c7\u30fc\u30bf\u304b\u3089\u5e73\u5747\u30fb\u5206\u6563\u30fb\u6a19\u6e96\u504f\u5dee<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. \u5ea6\u6570\u5206\u5e03\u8868<\/span>\u3092\u4f5c\u308a\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u5ea6\u6570\u6298\u7dda<\/span>\u3092\u304b\u304f\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n
1Q2H_3<\/span><\/a><\/td>\n1Q2H_E3<\/span><\/a><\/td>\n1Q2H_ES3<\/span><\/a><\/td>\n1Q2H_K3<\/span><\/a><\/td>\n1Q2H_V3<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
<\/span> \u30c7\u30fc\u30bf\uff5b$ 15,30,30,30,45,45,45,60,60 $\uff5d\u306b\u3064\u3044\u3066\u3001\u5e73\u5747\u30fb\u5206\u6563$=?$ <\/div>
(\u516c\u5f0f1)\u3000\u5206\u6563\u3000$V(x)=E(x^2)-E(x)^2$<\/span>$=$\u300c(\uff12\u4e57\u306e\u5e73\u5747)-(\u5e73\u5747)$^2$\u300d
(\u516c\u5f0f2)\u3000$E(ay+b)=aE(y)+b$<\/span>\u3001$V(ay+b)=a^2V(y)$<\/span>
\u8a3c\u660e\uff1a1Q2H_V3_pf<\/span><\/a><\/p>\n\n\n\n\n\n\n
$x$<\/td>\n15<\/td>\n30<\/td>\n45<\/td>\n60<\/td>\n\u8a08<\/td>\n<\/tr>\n
$f$<\/td>\n1<\/td>\n3<\/td>\n3<\/td>\n2<\/td>\n9<\/td>\n<\/tr>\n
$xf$<\/td>\n15<\/td>\n90<\/td>\n135<\/td>\n120<\/td>\n360<\/td>\n<\/tr>\n
$x^2f$<\/td>\n225<\/td>\n2700<\/td>\n6075<\/td>\n7200<\/td>\n16200<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5e73\u5747<\/span>\u3000$E(x)=\\dfrac{1}{n} \\Sigma xf=\\dfrac{1}{9} \\cdot 360=40$
$E(x^2)=\\dfrac{1}{n} \\Sigma x^2f=\\dfrac{1}{9} \\cdot 16200=1800$ \u3088\u308a
\u5206\u6563<\/span>\u3000$V(x)=E(x^2)-E(x)^2=1800-40^2=200$
$y=\\dfrac{x-45}{15} \\; (x=15y+45)$<\/span> \u3068\u5909\u6570\u5909\u63db<\/span>\u3059\u308b\u3068<\/span><\/p>\n\n\n\n\n\n\n
$y$<\/td>\n-2<\/td>\n-1<\/td>\n0<\/td>\n1<\/td>\n\u8a08<\/td>\n<\/tr>\n
$f$<\/td>\n1<\/td>\n3<\/td>\n3<\/td>\n2<\/td>\n9<\/td>\n<\/tr>\n
$yf$<\/td>\n-2<\/td>\n-3<\/td>\n0<\/td>\n2<\/td>\n-3<\/td>\n<\/tr>\n
$y^2f$<\/td>\n4<\/td>\n3<\/td>\n0<\/td>\n2<\/td>\n9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

$E(y)$<\/span>$=\\dfrac{1}{n} \\Sigma yf=\\dfrac{1}{9} \\cdot (-3)=\\dfrac{-1}{3}$\u3000$E(y^2)=\\dfrac{1}{n} \\Sigma y^2f=\\dfrac{1}{9} \\cdot 9=1$
\u3088\u3063\u3066\u3001$V(y)$<\/span>$=E(y^2)-E(y)^2=1-\\Big( \\dfrac{-1}{3}\\Big)^2=\\dfrac{8}{9}$
$x=15y+45$\u3088\u308a
\u5e73\u5747<\/span>\u3000$E(x)=E(15y+45)=15$$E(y)$<\/span>$+45=15\\cdot \\dfrac{-1}{3}+45=40$
\u5206\u6563<\/span>\u3000$V(x)=V(15y+45)=15^2$$V(y)$<\/span>$=15^2\\cdot \\dfrac{8}{9}=200$<\/div><\/div>

<\/span>Targets<\/div>
1. \u62e1\u5f35\u3057\u305f\u5ea6\u6570\u5206\u5e03\u8868<\/span>\u3092\u5229\u7528\u3057\u3066\u3001\u5e73\u5747\u3068\u5206\u6563<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. \u5909\u6570\u5909\u63db<\/span>\u3092\u5229\u7528\u3057\u3066\u5e73\u5747\u3068\u5206\u6563<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0 \u00a0 \u00a0 Next \u00a0 \u00a0 \u00a0 \u00a0 \u518d\u751f\u30ea\u30b9\u30c8 \u30c6\u30ad\u30b9\u30c8 \u6f14\u7fd2 \u6f14\u7fd2\u89e3\u7b54 \u8ab2\u984c \u89e3\u8aac 1Q2H_1 1Q2H_E1 1Q2H_ES1 1Q2H_K1 1Q2H_V1 1Q2H_2 1Q2H_E2 1Q2H_ES2 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,40,14,4,7],"tags":[],"class_list":["post-790","post","type-post","status-publish","format-standard","hentry","category-si","category-math2-1q2h","category-top","category-math2","category-math2-1q"],"_links":{"self":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/790","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=790"}],"version-history":[{"count":15,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/790\/revisions"}],"predecessor-version":[{"id":1875,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/790\/revisions\/1875"}],"wp:attachment":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}