<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/fee14d77-79e1-4739-9cc1-2d14a1d0feff/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1d wsc"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1d wsc">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls1d wsc"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls1d wsc">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls1d wsc"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls1d wsc">MEDIDAS RESUMO </div><div class="t m0 x1 h6 y8 ff3 fs3 fc1 sc0 ls1d wsc">Notações </div><div class="t m0 x3 h7 y9 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> </span><span class="ff6">\ue754</span></div><div class="t m0 x4 h8 ya ff6 fs5 fc0 sc0 ls1">\ueb35<span class="fs4 ls1d ws1 v1">, \ue754</span><span class="ls2">\ueb36<span class="fs4 ls1d ws1 v1">, \u2026 , \ue754<span class="_0 blank"></span><span class="fs5 ls3 v2">\uebe1<span class="ff2 fs4 ls1d wsc v1"> são <span class="ff6 ls4">\ue74a</span> observações de uma variável X (amostra de X). </span></span></span></span></div><div class="t m0 x3 h7 yb ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> </span><span class="ff6 ws2">\ue754<span class="fs5 ls5 v3">(</span><span class="fs5 ws3 v2">\ueb35<span class="ls6 v4">)</span></span><span class="ws1">, \ue754<span class="_0 blank"></span><span class="fs5 ls5 v3">(<span class="ls1d ws3 v5">\ueb36</span><span class="ls6">)<span class="fs4 ls1d ws4 v6">, \u2026 , \ue754</span></span>(<span class="ls7 v5">\uebe1</span><span class="ls6">)<span class="ff2 fs4 ls1d wsc v6"> são estatísticas de ordem, onde <span class="ff6 ws2">\ue754</span></span></span>(<span class="ls1d ws3 v5">\ueb35</span><span class="ls8">)<span class="fs4 ls1d ws5 v6">< \ue754<span class="_0 blank"></span><span class="fs5 ls5 v3">(<span class="ls1d ws3 v5">\ueb36</span><span class="ls9">)<span class="fs4 ls1d v6">< \u22ef < \ue754</span></span>(<span class="ls7 v5">\uebe1</span><span class="lsa">)<span class="ff2 fs4 ls1d wsc v6">. </span></span></span></span></span></span></span></span></div><div class="t m0 x3 h7 yc ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff6 ls4">\ue74a<span class="ff2 ls1d"> \u2013 Total de observações da variável (Tamanho da amostra). </span></span></span></div><div class="t m0 x1 h9 yd ff3 fs3 fc1 sc0 ls1d wsc">Moda (<span class="ff6 ws6">\ue89e<span class="fs6 lsb v7">\u2217</span></span>) </div><div class="t m0 x3 ha ye ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Valor com maior frequência. </span></span></div><div class="t m0 x3 ha yf ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Variáveis qualitativas e quantitativas. </span></span></div><div class="t m0 x1 hb y10 ff3 fs3 fc1 sc0 ls1d wsc">Mediana (<span class="ff6 lsc">\ue897<span class="fs6 lsd v8">\ueadb</span></span>) </div><div class="t m0 x3 ha y11 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Valor central ao ordenar os dados. </span></span></div><div class="t m0 x3 h7 y12 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Metade das observações é menor que <span class="ff6 ws2">\ue74d<span class="_0 blank"></span><span class="fs5 ls2 v2">\ueb36<span class="ff2 fs4 ls1d wsc v1"> e metade das observações é maior </span></span></span></span></span></div><div class="t m0 x5 h7 y13 ff2 fs4 fc0 sc0 lse wsc">que <span class="ff6 ls1d ws2">\ue74d<span class="_0 blank"></span><span class="fs5 ls2 v2">\ueb36<span class="ff2 fs4 ls1d wsc v1">. </span></span></span></div><div class="t m0 x1 h6 y14 ff3 fs3 fc1 sc0 ls1d wsc">Se n for par </div><div class="t m0 x6 hc y15 ff6 fs4 fc0 sc0 ls1d ws2">\ue74d<span class="fs5 lsf v2">\ueb36</span><span class="ls10">=</span><span class="v9">\ue754<span class="_0 blank"></span><span class="fs5 ls11 va">\uf240<span class="ls1d v7">\uebe1</span></span></span></div><div class="t m0 x7 hd y16 ff6 fs5 fc0 sc0 ls12">\ueb36<span class="ls13 vb">\uf241</span><span class="fs4 ls1d ws7 vc">+ \ue754</span><span class="ls11 vb">\uf240</span><span class="ls1d vc">\uebe1</span></div><div class="t m0 x8 he y16 ff6 fs5 fc0 sc0 ls12">\ueb36<span class="ls1d ws3 vb">\ueb3e\ueb35\uf241</span></div><div class="t m0 x9 hf y17 ff6 fs4 fc0 sc0 ls14">2<span class="ff2 ls1d wsc vd"> </span></div><div class="t m0 x1 h6 y18 ff3 fs3 fc1 sc0 ls1d wsc">Se n for ímpar </div><div class="t m0 xa h7 y19 ff6 fs4 fc0 sc0 ls1d ws2">\ue74d<span class="fs5 lsf v2">\ueb36</span><span class="ws8">= \ue754<span class="fs5 ls11 ve">\uf240</span><span class="fs5 ws3 vf">\uebe1\ueb3e\ueb35</span></span></div><div class="t m0 xb h10 y1a ff6 fs5 fc0 sc0 ls15">\ueb36<span class="ls16 vb">\uf241</span><span class="ff2 fs4 ls1d wsc v10"> </span></div><div class="t m0 x1 h6 y1b ff3 fs3 fc1 sc0 ls1d wsc">Média amostral </div><div class="t m0 xc h7 y1c ff6 fs4 fc0 sc0 ls1d">\ue89e</div><div class="t m0 xc h11 y1d ff6 fs4 fc2 sc0 ls17">\ued25<span class="fc0 ls18 v5">=<span class="ls1d vc">\ueada</span></span></div><div class="t m0 xd h12 y1e ff6 fs4 fc0 sc0 ls19">\ue894<span class="fc2 ls1a vd">\uedcd</span><span class="ls1d ws2 vd">\ue89e<span class="fs5 v2">\ue88f</span></span></div><div class="t m0 xe h13 y1f ff6 fs5 fc0 sc0 ls1d">\ue894</div><div class="t m0 xf h13 y20 ff6 fs5 fc0 sc0 ls1d ws3">\ue88f\ueb40\ueada</div><div class="t m0 x10 ha y1c ff2 fs4 fc0 sc0 ls1d wsc">, se usar dados brutos. </div><div class="t m0 x11 h14 y21 ff6 fs4 fc0 sc0 ls1d ws9">\ue754<span class="_0 blank"></span>\u0305<span class="_1 blank"> </span>= <span class="vc">1</span></div><div class="t m0 x12 h12 y22 ff6 fs4 fc0 sc0 ls1b">\ue74a<span class="ls1d wsa vd">\uedcd \ue754</span><span class="fs5 ls1c v11">\uebdc</span><span class="lse vd">\ue74a</span><span class="fs5 ls1d v11">\uebdc</span></div><div class="t m0 x13 h13 y23 ff6 fs5 fc0 sc0 ls1d">\uebde</div><div class="t m0 x14 h15 y24 ff6 fs5 fc0 sc0 ls1d wsb">\uebdc \ueb40\ueb35<span class="_2 blank"> </span><span class="fs4 wsa v12">=<span class="_3 blank"> </span>\uedcd \ue754</span><span class="ls1c v13">\uebdc</span><span class="fs4 v12">\ue742</span></div><div class="t m0 x15 h13 y25 ff6 fs5 fc0 sc0 ls1d">\uebdc</div><div class="t m0 x8 h13 y23 ff6 fs5 fc0 sc0 ls1d">\uebde</div><div class="t m0 x16 h13 y24 ff6 fs5 fc0 sc0 ls1d wsb">\uebdc \ueb40\ueb35</div><div class="t m0 x17 ha y21 ff2 fs4 fc0 sc0 ls1d wsc">, </div><div class="t m0 x1 ha y26 ff2 fs4 fc0 sc0 ls1d wsc">onde k é o número de valores assumidos pela variável, se usar distri<span class="_0 blank"></span>buição de frequência.<span class="_4 blank"> </span> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/fee14d77-79e1-4739-9cc1-2d14a1d0feff/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1d wsc"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1d wsc">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls1d wsc"> </div></div><div class="t m0 x1 h6 y27 ff3 fs3 fc1 sc0 ls1d wsc">Separatrizes ou quantis </div><div class="t m0 x1 h7 y28 ff2 fs4 fc0 sc0 ls1d wsc">O quantil de ordem p, (<span class="ff6 ls1e wsd">0<\ue74c<1<span class="_5 blank"></span><span class="ff2 ls1d wsc">), denotado por <span class="ff6 wse">\ue74d (\ue74c)</span> é um valor tal que pelo menos </span></span></div><div class="t m0 x1 h16 y29 ff6 fs4 fc0 sc0 ls1d ws2">100\ue74c%<span class="ff2 wsc"> das observações são menores que ele e pelo m<span class="_0 blank"></span>enos <span class="_4 blank"> </span><span class="ff6 ws2">100<span class="v4">(</span><span class="wsf">1 \u2212 \ue74c</span><span class="v4">)</span>%</span> das </span></div><div class="t m0 x1 ha y2a ff2 fs4 fc0 sc0 ls1d wsc">observações são maiores que ele. </div><div class="t m0 x3 h7 y2b ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Quartis: <span class="ff6">\ue74d</span></span></span></div><div class="t m0 x18 h17 y2c ff6 fs5 fc0 sc0 lsf">\ueb35<span class="fs4 ls1d wse v1">=<span class="_3 blank"> </span>\ue74d <span class="ws2 v4">(<span class="v5">0,25</span>)<span class="ws10 v5">, \ue74d</span></span></span>\ueb36<span class="fs4 ls1d wse v1">=<span class="_3 blank"> </span>\ue74d<span class="ws2 v4">(<span class="v5">0,50</span>)<span class="ws10 v5">, \ue74d</span></span></span>\ueb37<span class="fs4 ls1d wse v1">=<span class="_3 blank"> </span>\ue74d (0,75)<span class="ff2 wsc"> \u2013 Dividem o conjunto de </span></span></div><div class="t m0 x5 ha y2d ff2 fs4 fc0 sc0 ls1d wsc">dados em 4 partes iguais. </div><div class="t m0 x3 h7 y2e ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Decis: <span class="ff6">\ue740</span></span></span></div><div class="t m0 x19 h17 y2f ff6 fs5 fc0 sc0 lsf">\ueb35<span class="fs4 ls1d ws11 v1">=<span class="_3 blank"> </span>\ue74d <span class="ws2 v4">(<span class="v5">0,10</span>)<span class="ws4 v5">, \ue740</span></span></span>\ueb36<span class="fs4 ls1d wse v1">=<span class="_3 blank"> </span>\ue74d <span class="ws2 v4">(<span class="v5">0,20</span>)<span class="wsc v5">,<span class="_6 blank"> </span>\u2026<span class="_7 blank"> </span> <span class="_7 blank"> </span>,<span class="_6 blank"> </span>\ue740</span></span></span><span class="ls1f">\ueb3d<span class="fs4 ls1d wsc v1">=<span class="_3 blank"> </span>\ue74d<span class="_4 blank"> </span>(0,90) <span class="ff2">\u2013 Dividem o conjunto de </span></span></span></div><div class="t m0 x5 ha y30 ff2 fs4 fc0 sc0 ls1d wsc">dados em 10 partes iguais. </div><div class="t m0 x3 h7 y31 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Percentis: <span class="ff6">\ue74c</span></span></span></div><div class="t m0 x1a h17 y32 ff6 fs5 fc0 sc0 ls20">\ueb35<span class="fs4 ls1d wse v1">=<span class="_3 blank"> </span>\ue74d <span class="ws2 v4">(</span><span class="lse ws12">0,01<span class="ls1d ws2 v4">)</span><span class="ls1d ws4">, \ue74c</span></span></span></div><div class="t m0 x6 h17 y32 ff6 fs5 fc0 sc0 ls20">\ueb36<span class="fs4 ls1d ws11 v1">=<span class="_3 blank"> </span>\ue74d <span class="ws2 v4">(<span class="v5">0,02</span>)<span class="ws4 v5">, \u2026 , \ue74c</span></span></span></div><div class="t m0 x1b h8 y32 ff6 fs5 fc0 sc0 ls1d ws13">\ueb3d\ueb3d <span class="fs4 wse v1">=<span class="_3 blank"> </span>\ue74d (0,99)<span class="ff2 wsc"> \u2013 Dividem o conjunto </span></span></div><div class="t m0 x5 ha y33 ff2 fs4 fc0 sc0 ls1d wsc">de dados em 100 partes iguais. </div><div class="t m0 x1 h6 y34 ff3 fs3 fc1 sc0 ls1d wsc">Cálculo de quartis </div><div class="t m0 x3 ha y35 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Ordenar os dados. </span></span></div><div class="t m0 x3 ha y36 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Encontrar a mediana. </span></span></div><div class="t m0 x3 h7 y37 ff4 fs4 fc0 sc0 ls1d ws0">\uf0b7<span class="ff5 ls0 wsc"> <span class="ff2 ls1d">Encontrar a mediana das observações menores que a median<span class="_0 blank"></span>a, que é <span class="_4 blank"> </span><span class="ff6">\ue74d</span></span></span></div><div class="t m0 x1c h18 y38 ff6 fs5 fc0 sc0 ls1">\ueb35<span class="ff2 fs4 ls1d wsc v1">e a </span></div><div class="t m0 x5 h7 y39 ff2 fs4 fc0 sc0 ls1d wsc">mediana das observações maiores que a mediana, que é <span class="ff6 ws2">\ue74d<span class="_0 blank"></span><span class="fs5 ls2 v2">\ueb37<span class="ff2 fs4 ls1d wsc v1">. </span></span></span></div><div class="t m0 x1 h6 y3a ff3 fs3 fc1 sc0 ls1d wsc">Propriedades </div><div class="t m0 x1 ha y3b ff2 fs4 fc0 sc0 ls1d wsc">Ao se somar ou multiplicar um mesmo valor à todas as obs<span class="_0 blank"></span>ervações, a moda, média e </div><div class="t m0 x1 ha y3c ff2 fs4 fc0 sc0 ls1d wsc">mediana são somadas ou multiplicadas pelo mesmo valor. </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls1d wsc"> </div><div class="t m0 x1 h2 y3e ff1 fs0 fc0 sc0 ls1d wsc"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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