<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/95218c41-edd6-4b38-8de3-ad1fbdfa7fb8/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsf ws7">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 lsf ws7">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 lsf ws7"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 lsf ws7">EXERCÍCIOS </div><div class="t m0 x1 h6 y8 ff3 fs3 fc1 sc0 lsf ws7">Desempenho dos carros </div><div class="t m0 x1 h7 y9 ff2 fs4 fc0 sc0 lsf ws7">Foram realizados 5 testes com 3 marcas de carro do mesmo segmento, que possue<span class="_0 blank"></span>m </div><div class="t m0 x1 h8 ya ff2 fs4 fc0 sc0 lsf ws7">tanques de <span class="ff4 ws0">40\ue748 </span> e verificou-se a quilometragem percorrida pelos carros com a </div><div class="t m0 x1 h7 yb ff2 fs4 fc0 sc0 lsf ws7">quantidade de combustível suportada pelos tanques. </div><div class="t m0 x3 h7 yc ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h7 yd ff2 fs4 fc0 sc0 lsf ws7">Compare o desempenho dos 3 carros. </div><div class="t m0 x4 h7 ye ff2 fs4 fc1 sc0 lsf ws7">Resolução: </div><div class="t m0 x1 h7 yf ff2 fs4 fc0 sc0 lsf ws7">Vamos chamar de A a variável definida pela distância (em km) percorrida pelo carro <span class="_0 blank"></span>da </div><div class="t m0 x1 h7 y10 ff2 fs4 fc0 sc0 lsf ws7">marca A com o tanque. O mesmo pra B e C. </div><div class="t m0 x1 h7 y11 ff2 fs4 fc0 sc0 lsf ws7">Vamos calcular a média amostral de A, B e de C. </div><div class="t m0 x5 h9 y12 ff4 fs4 fc0 sc0 lsf ws1">\ue723<span class="ls0 v1">\u0305</span><span class="ls1">=</span><span class="ws2 v2">400 + 397 + 401<span class="_1 blank"> </span>+ 389 + 403</span></div><div class="t m0 x6 ha y13 ff4 fs4 fc0 sc0 ls2">5<span class="lsf ws7 v3">=<span class="_2 blank"> </span>398 \ue747\ue749<span class="ff2"> </span></span></div><div class="t m0 x7 h8 y14 ff4 fs4 fc0 sc0 lsf">\ue724</div><div class="t m0 x8 hb y15 ff4 fs4 fc0 sc0 ls3">\ued24<span class="ls1 v4">=</span><span class="lsf ws2 v5">403 + 401 + 390 + 378 + 395</span></div><div class="t m0 x9 ha y16 ff4 fs4 fc0 sc0 ls2">5<span class="lsf ws7 v3">=<span class="_2 blank"> </span>393,4 \ue747\ue749<span class="ff2"> </span></span></div><div class="t m0 x7 h9 y17 ff4 fs4 fc0 sc0 lsf ws1">\ue725<span class="ls4 v1">\u0305</span><span class="ls5">=</span><span class="ws2 v2">399 + 389 + 403 + 387 + 401</span></div><div class="t m0 x9 ha y18 ff4 fs4 fc0 sc0 ls2">5<span class="lsf ws7 v3">=<span class="_2 blank"> </span>395,8 \ue747\ue749<span class="_3 blank"> </span><span class="ff2"> </span></span></div><div class="t m0 x1 h7 y19 ff2 fs4 fc0 sc0 lsf ws7">Em média, o carro da marca A percorre uma dist<span class="_0 blank"></span>ância maior que os carros das marcas </div><div class="t m0 x1 h7 y1a ff2 fs4 fc0 sc0 lsf ws7">B e C com um tanque de combustível. </div><div class="t m0 x1 h7 y1b ff2 fs4 fc0 sc0 lsf ws7">Precisamos comparar a variabilidade. </div><div class="t m0 xa hc y1c ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls6">\ue723<span class="ls7 v6">)</span><span class="ls8">=</span></span><span class="ff2 ws7"> </span></div><div class="t m0 xb h8 y1d ff4 fs4 fc0 sc0 lsf ws1">(<span class="ws4 v7">400 \u2212 398</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsa v7">+</span>(<span class="ws4 v7">397 \u2212 398</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws5 v7">401 \u2212 398</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">38<span class="_3 blank"> </span>9 \u2212 398</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws5 v7">403 \u2212 398</span>)<span class="fs5 v8">\ueb36</span></div><div class="t m0 xc hd y1e ff4 fs4 fc0 sc0 lsf ws6">5 \u2212 1<span class="_4 blank"> </span><span class="ff2 ws7 v3"> </span></div><div class="t m0 xd hc y1f ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls6">\ue723<span class="ls7 v6">)</span></span><span class="ws7">=<span class="_2 blank"> </span>30 \ue747<span class="_3 blank"> </span>\ue749<span class="_3 blank"> </span><span class="fs5 lsc v9">\ueb36</span><span class="ff2"> </span></span></div><div class="t m0 xa hc y20 ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="lsd">\ue724<span class="lse v6">)</span><span class="ls8">=</span></span><span class="ff2 ws7"> </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/95218c41-edd6-4b38-8de3-ad1fbdfa7fb8/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsf ws7">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="t m0 x1 h8 y21 ff4 fs4 fc0 sc0 lsf ws1">(<span class="ws4 v7">403 \u2212 393,4</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">401 \u2212 393,4</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">390 \u2212 393,4</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">378 \u2212 39<span class="_3 blank"> </span>3,4</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsa v7">+</span>(<span class="ws4 v7">395 \u2212 393,4</span>)<span class="fs5 v8">\ueb36</span></div><div class="t m0 xe hd y22 ff4 fs4 fc0 sc0 lsf ws2">5 \u2212 1<span class="_5 blank"> </span><span class="ff2 ws7 v3"> </span></div><div class="t m0 xf hc y23 ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="lsd">\ue724<span class="lse v6">)</span></span><span class="ws7">=<span class="_2 blank"> </span>100,3 \ue747<span class="_3 blank"> </span>\ue749<span class="_3 blank"> </span><span class="fs5 ls11 v9">\ueb36</span><span class="ff2"> </span></span></div><div class="t m0 xa hc y24 ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls12">\ue725<span class="ls7 v6">)</span><span class="ls8">=</span></span><span class="ff2 ws7"> </span></div><div class="t m0 x1 h8 y25 ff4 fs4 fc0 sc0 lsf ws1">(<span class="ws4 v7">399 \u2212 395,8</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">389 \u2212 395,8</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">403 \u2212 395,8</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws4 v7">387 \u2212 39<span class="_3 blank"> </span>5,8</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsa v7">+</span>(<span class="ws4 v7">401 \u2212 395,8</span>)<span class="fs5 v8">\ueb36</span></div><div class="t m0 xe hd y26 ff4 fs4 fc0 sc0 lsf ws2">5 \u2212 1<span class="_5 blank"> </span><span class="ff2 ws7 v3"> </span></div><div class="t m0 x10 hc y27 ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls12">\ue725<span class="ls7 v6">)</span></span><span class="ws7">=<span class="_2 blank"> </span>53,2 \ue747<span class="_3 blank"> </span>\ue749<span class="_3 blank"> </span><span class="fs5 ls11 v9">\ueb36</span><span class="ff2"> </span></span></div><div class="t m0 x1 h7 y28 ff2 fs4 fc0 sc0 lsf ws7">Ou, outra maneira de calcular a variância: </div><div class="t m0 x11 he y29 ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls6">\ue723<span class="lse v6">)</span><span class="ls1">=</span></span><span class="ws1 v2">400</span><span class="fs5 ls9 va">\ueb36</span><span class="ws6 v2">+ 397</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 401</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 389</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 403</span><span class="fs5 ls9 va">\ueb36</span><span class="ws8 v2">\u2212 5 × 398</span><span class="fs5 va">\ueb36</span></div><div class="t m0 xc hf y2a ff4 fs4 fc0 sc0 lsf ws8">5 \u2212 1<span class="_6 blank"> </span><span class="ws7 v3">=<span class="_2 blank"> </span>30 \ue747<span class="_3 blank"> </span>\ue749<span class="_3 blank"> </span></span><span class="fs5 lsc vb">\ueb36</span><span class="ff2 ws7 v3"> </span></div><div class="t m0 x12 he y2b ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="lsd">\ue724<span class="ls13 v6">)</span><span class="ls5">=</span></span><span class="ws1 v2">403</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 401</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 390</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 378</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 395</span><span class="fs5 ls9 va">\ueb36</span><span class="ws6 v2">\u2212 5<span class="_7 blank"> </span>× 393,4</span><span class="fs5 va">\ueb36</span></div><div class="t m0 x13 hf y2c ff4 fs4 fc0 sc0 lsf ws2">5 \u2212 1<span class="_8 blank"> </span><span class="ws7 v3">=<span class="_2 blank"> </span>100,3 \ue747<span class="_3 blank"> </span>\ue749<span class="_3 blank"> </span></span><span class="fs5 lsc vb">\ueb36</span><span class="ff2 ws7 v3"> </span></div><div class="t m0 x14 he y2d ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls12">\ue725<span class="lse v6">)</span><span class="ls1">=</span></span><span class="ws1 v2">399</span><span class="fs5 ls9 va">\ueb36</span><span class="ws6 v2">+ 389</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 403</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 387</span><span class="fs5 ls9 va">\ueb36</span><span class="ws2 v2">+ 401</span><span class="fs5 ls9 va">\ueb36</span><span class="ws8 v2">\u2212 5 × 395,8</span><span class="fs5 va">\ueb36</span></div><div class="t m0 x6 hf y2e ff4 fs4 fc0 sc0 lsf ws8">5 \u2212 1<span class="_8 blank"> </span><span class="ws7 v3">=<span class="_2 blank"> </span>53,2 \ue747<span class="_3 blank"> </span>\ue749<span class="_3 blank"> </span></span><span class="fs5 ls11 vb">\ueb36</span><span class="ff2 ws7 v3"> </span></div><div class="t m0 x1 h7 y2f ff2 fs4 fc0 sc0 lsf ws7">Podemos perceber que a variância de A é a menor dentre as 3. </div><div class="t m0 x1 h7 y30 ff2 fs4 fc0 sc0 lsf ws7">Como tem a maior média e menor variância da distânci<span class="_0 blank"></span>a percorrida com um tanque, o </div><div class="t m0 x1 h7 y31 ff2 fs4 fc0 sc0 lsf ws7">carro da marca A pode ser considerado, com base nessa amostra, como sendo mais </div><div class="t m0 x1 h7 y32 ff2 fs4 fc0 sc0 ls14 ws7">eficiente. </div><div class="t m0 x1 h6 y33 ff3 fs3 fc1 sc0 lsf ws7">Medidas de pacientes </div><div class="t m0 x1 h7 y34 ff2 fs4 fc0 sc0 lsf ws7">Num grupo de pacientes, foram tomadas as pulsações (batidas por minuto) e </div><div class="t m0 x1 h8 y35 ff2 fs4 fc0 sc0 lsf ws7">verificadas as taxas de ácido úrico (<span class="ff4 ws9">\ue749\ue743/100\ue749\ue748 </span>).<span class="_3 blank"> </span> </div><div class="t m0 x15 h7 y36 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h7 y37 ff2 fs4 fc0 sc0 lsf ws7">Qual a medida mais estável? </div><div class="t m0 x1 h10 y38 ff2 fs4 fc1 sc0 lsf wsa">Resolução:<span class="ff3 ws7"> </span></div><div class="t m0 x1 h7 y39 ff2 fs4 fc0 sc0 lsf ws7">O exercício quer comparar a variabilidade de X e de Y, mas elas têm unidade </div><div class="t m0 x1 h7 y3a ff2 fs4 fc0 sc0 lsf ws7">diferentes. Usaremos então o coeficiente de v<span class="_0 blank"></span>ariação.<span class="fc2"> </span></div><div class="t m0 x16 h8 y3b ff4 fs4 fc0 sc0 lsf">\ue89e</div><div class="t m0 x16 h11 y3c ff4 fs4 fc0 sc0 ls1">\ued25<span class="v7">=</span><span class="lsf ws2 v2">\ueae2\ueada + \ueada\ueada\ueadb + \ueae1\ueadb + \ueadf\ueae0 + \ueada\ueada\ueadb + \ueada\uead9\ueade + \ueae0\ueadc + \ueadf\ueadc + \ueae2\ueade + \ueae2\ueade</span></div><div class="t m0 x17 ha y3d ff4 fs4 fc0 sc0 lsf wsb">\ueada\uead9 <span class="wsc v3">\u2248<span class="_2 blank"> </span>\ueae1\ueae2, \ueade<span class="ff2 ws7"> </span></span></div><div class="t m0 x1 hc y3e ff4 fs4 fc0 sc0 lsf ws1">\ue882\ue887\ue898<span class="v6">(</span>\ue884<span class="v6">)</span></div><div class="t m0 x1 he y3f ff4 fs4 fc0 sc0 ls1">=<span class="lsf ws1 v2">\ueae2\ueada</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws2 v2">+ \ueada\ueada\ueadb</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws2 v2">+ \ueae1\ueadb</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws6 v2">+ \ueadf\ueae0</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws2 v2">+ \ueada\ueada\ueadb</span><span class="fs5 ls16 va">\ueadb</span><span class="lsf ws2 v2">+ \ueada\uead9<span class="_3 blank"> </span>\ueade</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws6 v2">+ \ueae0\ueadc</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws2 v2">+ \ueadf\ueadc</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws2 v2">+ \ueae2\ueade</span><span class="fs5 ls16 va">\ueadb</span><span class="lsf ws2 v2">+ \ueae2\ueade</span><span class="fs5 ls15 va">\ueadb</span><span class="lsf ws2 v2">\u2212 \ueada\uead9 × \ueae1\ueae2,<span class="_1 blank"> </span>\ueade<span class="fs5 v9">\ueadb</span></span></div><div class="t m0 x18 h12 y40 ff4 fs4 fc0 sc0 ls17">\ueae2<span class="ff3 lsf ws7 v3"> </span></div><div class="t m0 x19 hc y41 ff4 fs4 fc0 sc0 lsf ws1">\ue882\ue887\ue898<span class="v6">(</span>\ue884<span class="lse v6">)</span><span class="wsd">\u2248<span class="_2 blank"> </span>\ueadc\ueada\ueadf, \ueae1\ueadd<span class="_2 blank"> </span>\u21d2<span class="_2 blank"> </span>\ue870\ue87c</span><span class="v6">(</span>\ue884<span class="lse v6">)</span><span class="ls1">=<span class="ls18 v0">\ueda5</span></span><span class="wse">\ueadc\ueada\ueadf,<span class="_9 blank"> </span>\ueae1\ueadd = \ueada\ueae0,<span class="_9 blank"> </span>\ueae1<span class="ff3 ws7"> </span></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="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/95218c41-edd6-4b38-8de3-ad1fbdfa7fb8/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsf ws7">3 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="t m0 x1a h9 y42 ff4 fs4 fc0 sc0 lsf ws1">\ue86f\ue882<span class="v6">(</span>\ue884<span class="lse v6">)</span><span class="ls1">=</span><span class="wsd v2">\ueada\ueae0, \ueae1</span></div><div class="t m0 x1b ha y43 ff4 fs4 fc0 sc0 lsf wsd">\ueae1\ueae2, \ueade<span class="_2 blank"> </span><span class="v3">\u2248<span class="_2 blank"> </span>\uead9, \ueada\ueae2\ueae2<span class="ff3 ws7"> </span></span></div><div class="t m0 x1 h10 y44 ff3 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1c h8 y45 ff4 fs4 fc0 sc0 lsf">\ue89f</div><div class="t m0 x1c h11 y46 ff4 fs4 fc0 sc0 ls19">\ued25<span class="ls1 v7">=</span><span class="lsf ws2 v2">\ueadd,<span class="_9 blank"> </span>\ueadd\ueada + \ueadb,<span class="_a blank"> </span>\ueadf\ueadc + \ueadb,<span class="_a blank"> </span>\ueadb\ueae0 + \ueadb,<span class="_9 blank"> </span>\ueadc\ueae0 + \ueae0,<span class="_a blank"> </span>\uead9\ueadc + \ueadb,<span class="_9 blank"> </span>\ueae1\ueadd + \ueadf,<span class="_a blank"> </span>\ueada\ueadc + \ueadb,<span class="_9 blank"> </span>\ueadb\ueade + \ueae0,<span class="_a blank"> </span>\ueadd\uead9 + \ueadf<span class="_3 blank"> </span>,<span class="_a blank"> </span>\ueade\ueade</span></div><div class="t m0 x1d h8 y47 ff4 fs4 fc0 sc0 lsf ws1">\ueada\uead9</div><div class="t m0 x1e h8 y48 ff4 fs4 fc0 sc0 lsf wsd">\u2248<span class="_2 blank"> </span>\ueadd, \ueadd<span class="ff3 ws7"> </span></div><div class="t m0 x1 h10 y49 ff3 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 xa hc y4a ff4 fs4 fc0 sc0 lsf ws1">\ue882\ue887\ue898<span class="v6">(</span>\ue885<span class="lse v6">)</span>=<span class="ff3 ws7"> </span></div><div class="t m0 x1 h13 y4b ff4 fs4 fc0 sc0 lsf wsd">\ueadd, \ueadd\ueada<span class="fs5 ls15 v9">\ueadb</span>+<span class="_7 blank"> </span>\ueadb, \ueadf\ueadc<span class="fs5 ls16 v9">\ueadb</span>+<span class="_1 blank"> </span>\ueadb<span class="_3 blank"> </span>, \ueadb\ueae0<span class="fs5 ls15 v9">\ueadb</span>+<span class="_7 blank"> </span>\ueadb, \ueadc\ueae0<span class="fs5 ls16 v9">\ueadb</span>+<span class="_1 blank"> </span>\ueae0, \uead9\ueadc<span class="fs5 ls15 v9">\ueadb</span>+<span class="_7 blank"> </span>\ueadb, \ueae1\ueadd<span class="fs5 ls15 v9">\ueadb</span>+<span class="_7 blank"> </span>\ueadf, \ueada\ueadc<span class="fs5 ls15 v9">\ueadb</span>+<span class="_1 blank"> </span>\ueadb, \ueadb<span class="_3 blank"> </span>\ueade<span class="fs5 ls15 v9">\ueadb</span>+<span class="_7 blank"> </span>\ueae0, \ueadd\uead9<span class="fs5 ls16 v9">\ueadb</span>+<span class="_1 blank"> </span>\ueadf, \ueade\ueade<span class="fs5 ls15 v9">\ueadb</span>\u2212<span class="_7 blank"> </span>\ueada\uead9<span class="_7 blank"> </span>×<span class="_1 blank"> </span>\ueadd, \ueadd</div><div class="c x1f y4c w3 h14"><div class="t m0 x0 h15 y4d ff4 fs5 fc0 sc0 lsf">\ueadb</div></div><div class="t m0 x20 h8 y4e ff4 fs4 fc0 sc0 lsf">\ueae2</div><div class="t m0 x21 hc y4f ff4 fs4 fc0 sc0 lsf ws3">\ue738\ue73d\ue74e <span class="ws1 v6">(</span><span class="ls1a">\ue73b<span class="ls7 v6">)</span></span><span class="wsf">\u2248<span class="_2 blank"> </span>4,84<span class="_2 blank"> </span>\u21d2<span class="_2 blank"> </span>\ue726\ue732 <span class="ws1 v6">(</span><span class="ls1a">\ue73b<span class="ls7 v6">)</span><span class="ls1">=<span class="ls18 v0">\ueda5</span></span></span><span class="ws10">4,84 = 2,2<span class="ff2 fc2 ws7"> </span></span></span></div><div class="t m0 x22 h9 y50 ff4 fs4 fc0 sc0 lsf ws11">\ue725\ue738 <span class="ws1 v6">(</span><span class="ls1a">\ue73b<span class="ls7 v6">)</span><span class="ls1">=</span></span><span class="ws1 v2">2,2</span></div><div class="t m0 x23 ha y51 ff4 fs4 fc0 sc0 lsf ws12">4,4 <span class="wse v3">= 0,5<span class="ff2 ws7"> </span></span></div><div class="t m0 x1 hc y52 ff2 fs4 fc0 sc0 lsf ws7">Como <span class="ff4 ws11">\ue725\ue738 <span class="ws1 v6">(</span><span class="ls1b">\ue73a<span class="ls7 v6">)</span></span><span class="ws13"><<span class="_2 blank"> </span>\ue725\ue738 (\ue73b )</span></span>, então a medida Pulsação (X) é mais estável que a </div><div class="t m0 x1 h7 y53 ff2 fs4 fc0 sc0 lsf ws7">concentração de ácido úrico (Y). </div><div class="t m0 x1 h6 y54 ff3 fs3 fc1 sc0 lsf ws7">Medidas para dados agrupados </div><div class="t m0 x1 h7 y55 ff2 fs4 fc0 sc0 lsf ws7">Para os dados da tabela abaixo, calcule o coeficiente de variação, o intervalo </div><div class="t m0 x1 h7 y56 ff2 fs4 fc0 sc0 lsf ws7">interquartil e a moda, pelos métodos de King e Czuber. </div><div class="t m0 x24 h7 y57 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h7 y58 ff2 fs4 fc1 sc0 lsf ws7">Resolução: </div><div class="t m0 x1 h7 y1b ff2 fs4 fc0 sc0 lsf ws7">Chamemos essa variável de X. Para calcular o coeficiente de variação precisamos da </div><div class="t m0 x1 h7 y59 ff2 fs4 fc0 sc0 lsf ws7">média amostral e do desvio padrão. </div><div class="t m0 x25 h9 y5a ff4 fs4 fc0 sc0 lsf wse">\ue754<span class="_0 blank"></span>\u0305<span class="_b blank"> </span>= <span class="ws8 v2">0,5 × 15 + 1,5 × 26 + 2,5 × 21 + 3,5 × 10 + 4,5 × 8</span></div><div class="t m0 x26 ha y5b ff4 fs4 fc0 sc0 lsf ws14">80 <span class="wse v3">= 2,125<span class="ff2 ws7"> </span></span></div><div class="t m0 x1 h7 y5c ff2 fs4 fc0 sc0 lsf ws7">Ou, usando a frequência relativa: </div><div class="t m0 x27 h8 y5d ff4 fs4 fc0 sc0 lsf ws8">\ue754<span class="_0 blank"></span>\u0305<span class="_b blank"> </span>=<span class="_2 blank"> </span>0,5 × 0,1875 + 1,5 × 0,325 + 2,5 × 0,2625 + 3<span class="_3 blank"> </span>,5 × 0,125 + 4,5 × 0,1<span class="_2 blank"> </span>=<span class="_2 blank"> </span>2,125<span class="ff2 ws7"> </span></div><div class="t m0 x1b h13 y5e ff4 fs4 fc0 sc0 ls12">\ue74f<span class="fs5 ls1c v9">\ueb36</span><span class="ls8">=<span class="ff2 lsf ws7"> </span></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="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/95218c41-edd6-4b38-8de3-ad1fbdfa7fb8/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsf ws7">4 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="t m0 x1 h8 y21 ff4 fs4 fc0 sc0 lsf ws1">(<span class="ws8 v7">0,5 × 15 \u2212 2,125</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws8 v7">1,5 × 26 \u2212 2,125</span>)<span class="fs5 ls10 v8">\ueb36</span><span class="lsb v7">+</span>(<span class="ws5 v7">2,5<span class="_7 blank"> </span>× 21 \u2212 2,125</span>)<span class="fs5 ls9 v8">\ueb36</span><span class="ws15 v7">+<span class="_7 blank"> </span>\u22ef +<span class="_1 blank"> </span></span>(<span class="ws8 v7">4<span class="_3 blank"> </span>,5 × 8 \u2212 2,125</span>)<span class="fs5 v8">\ueb36</span></div><div class="t m0 x28 hd y22 ff4 fs4 fc0 sc0 lsf ws16">79 <span class="ff2 ws7 v3"> </span></div><div class="t m0 x29 h13 y23 ff4 fs4 fc0 sc0 ls12">\ue74f<span class="fs5 ls1c v9">\ueb36</span><span class="lsf ws17">\u2248 77,906<span class="ff2 ws7"> </span></span></div><div class="t m0 x2a h9 y5f ff4 fs4 fc0 sc0 lsf ws9">\ue725\ue738 <span class="ws1 v6">(</span><span class="ls1b">\ue73a<span class="lse v6">)</span><span class="ls1">=</span></span><span class="ws1 v3">\u221a<span class="vc">77,906</span></span></div><div class="t m0 x1b ha y60 ff4 fs4 fc0 sc0 lsf ws18">2,125 <span class="ws17 v3">\u2248 4,154<span class="ff2 ws7"> </span></span></div><div class="t m0 x1 h7 y61 ff2 fs4 fc0 sc0 lsf ws7">Para calcular o Intervalo interquartil vamos observar o histograma de X, junto com a </div><div class="t m0 x1 h7 y62 ff2 fs4 fc0 sc0 lsf ws7">frequência acumulada da tabela. </div><div class="t m0 x2b h7 y63 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x2c h8 y64 ff4 fs4 fc0 sc0 lsf">\ue74d</div><div class="t m0 x2d h16 y65 ff4 fs5 fc0 sc0 ls1c">\ueb35<span class="fs4 lsf ws19 v1">=<span class="_2 blank"> </span>\ue74d <span class="ws1 v6">(<span class="v7">0,25</span>)<span class="ff2 ls14 ws7 v7"> e </span><span class="v7">\ue74d</span></span></span><span class="ls1d">\ueb37<span class="fs4 lsf ws19 v1">=<span class="_2 blank"> </span>\ue74d(0,75 )<span class="ff2 ws7"> </span></span></span></div><div class="t m0 x1 h7 y66 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x2e h8 y67 ff4 fs4 fc0 sc0 lsf ws2">2 \u2212 1</div><div class="t m0 x2e h17 y68 ff4 fs4 fc0 sc0 lsf ws1a">0,325 <span class="ls1e v3">=</span><span class="vd">\ue74d</span></div><div class="t m0 x2f h18 y69 ff4 fs5 fc0 sc0 ls1f">\ueb35<span class="fs4 lsf ws2 v1">\u2212 1</span></div><div class="t m0 xf ha y68 ff4 fs4 fc0 sc0 lsf ws6">0,25 \u2212 0,1875<span class="_2 blank"> </span><span class="ws1b v3">\u21d2 \ue74d</span></div><div class="t m0 x30 h18 y6a ff4 fs5 fc0 sc0 ls20">\ueb35<span class="fs4 lsf wse v1">= 1,1923<span class="ff2 ws7"> </span></span></div><div class="t m0 x2e h8 y6b ff4 fs4 fc0 sc0 lsf ws6">3 \u2212 2</div><div class="t m0 x21 h17 y6c ff4 fs4 fc0 sc0 lsf ws10">0,2625 <span class="ls21 v3">=</span><span class="ws1 vd">\ue74d</span><span class="fs5 ls9 ve">\ueb37</span><span class="ws2 vd">\u2212 2</span></div><div class="t m0 x10 ha y6c ff4 fs4 fc0 sc0 lsf ws4">0,75 \u2212 0,5125<span class="_2 blank"> </span><span class="ws17 v3">\u21d2 \ue74d</span><span class="fs5 ls1d vf">\ueb37</span><span class="ws17 v3">\u2248 2,9048<span class="ff2 ws7"> </span></span></div><div class="t m0 x1 h7 y6d ff2 fs4 fc0 sc0 lsf ws7">Então: </div><div class="t m0 x31 hc y6e ff4 fs4 fc0 sc0 lsf ws9">\ue72b\ue733 <span class="ws1 v6">(</span><span class="ls1b">\ue73a<span class="lse v6">)</span></span><span class="ws2">=<span class="_2 blank"> </span>2,9048 \u2212 1,1923<span class="_2 blank"> </span>=<span class="_2 blank"> </span>1,7125<span class="ff2 ws7"> </span></span></div><div class="t m0 x1 h7 y6f ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h8 y70 ff2 fs4 fc0 sc0 lsf ws7">Observando o histograma, podemos perceber que a classe modal é <span class="ff4 ls22 ws1c">1\u22a22<span class="_c blank"></span><span class="ff2 lsf ws7">. </span></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="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/95218c41-edd6-4b38-8de3-ad1fbdfa7fb8/bg5.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsf ws7">5 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="t m0 x1 h7 y71 ff2 fs4 fc1 sc0 lsf ws7">Moda bruta: </div><div class="t m0 x32 h9 y72 ff4 fs4 fc0 sc0 ls23">\ue754<span class="fs5 ls24 v9">\u2217</span><span class="ls1">=<span class="lsf ws8 v2">1 + 2</span></span></div><div class="t m0 x33 ha y73 ff4 fs4 fc0 sc0 ls25">2<span class="lsf wse v3">= 1,5<span class="ff2 fc2 ws7"> </span></span></div><div class="t m0 x1 h7 y74 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h7 y75 ff2 fs4 fc1 sc0 lsf ws7">Moda de King: </div><div class="t m0 x34 h13 y76 ff4 fs4 fc0 sc0 ls23">\ue754<span class="fs5 ls26 v9">\u2217</span><span class="lsf ws2">\u2212 1</span></div><div class="t m0 x34 h17 y77 ff4 fs4 fc0 sc0 lsf ws1d">2<span class="_7 blank"> </span>\u2212<span class="_1 blank"> </span>\ue754 <span class="fs5 ls27 v10">\u2217</span><span class="ls5 v3">=</span><span class="ws1 vd">0.2625</span></div><div class="t m0 x29 hf y77 ff4 fs4 fc0 sc0 lsf wse">0.1875 <span class="ws1e v3">\u21d2<span class="_2 blank"> </span>\ue754 </span><span class="fs5 ls24 vb">\u2217</span><span class="ws17 v3">\u2248 1,583<span class="ff2 fc2 ws7"> </span></span></div><div class="t m0 x1 h7 y78 ff2 fs4 fc1 sc0 lsf ws7">Moda de Czuber: </div><div class="t m0 x35 h13 y79 ff4 fs4 fc0 sc0 ls28">\ue754<span class="fs5 ls26 v9">\u2217</span><span class="lsf ws2">\u2212 1</span></div><div class="t m0 x19 h19 y7a ff4 fs4 fc0 sc0 lsf ws4">0,325 \u2212 0,1875<span class="_2 blank"> </span><span class="ls29 v3">=</span><span class="ws1d vd">2<span class="_7 blank"> </span>\u2212<span class="_1 blank"> </span>\ue754 </span><span class="fs5 v11">\u2217</span></div><div class="t m0 x29 hf y7a ff4 fs4 fc0 sc0 lsf ws5">0,325 \u2212 0,2625<span class="_2 blank"> </span><span class="ws1d v3">\u21d2<span class="_2 blank"> </span>\ue754 </span><span class="fs5 ls27 vb">\u2217</span><span class="wse v3">= 1,6875<span class="ff2 fc2 ws7"> </span></span></div><div class="t m0 x1 h7 y7b ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h6 y7c ff3 fs3 fc1 sc0 lsf ws7">Desvio médio absoluto </div><div class="t m0 x1a h9 y7d ff4 fs4 fc0 sc0 lsf ws1">\ue726\ue72f\ue723<span class="v6">(</span><span class="ls2a">\ue754<span class="lse v6">)</span><span class="ls2b">=</span></span><span class="v2">1</span></div><div class="t m0 x36 ha y7e ff4 fs4 fc0 sc0 ls2c">\ue74a<span class="lsf ws1f v3">\uedcd |\ue754</span><span class="fs5 ls2d vf">\uebdc</span><span class="lsf ws20 v3">\u2212<span class="_1 blank"> </span>\ue754<span class="_0 blank"></span>\u0305 |</span></div><div class="t m0 x37 h15 y7f ff4 fs5 fc0 sc0 lsf">\uebe1</div><div class="t m0 x38 h15 y80 ff4 fs5 fc0 sc0 lsf ws21">\uebdc \ueb40\ueb35</div><div class="t m0 x39 h7 y7d ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h7 y81 ff2 fs4 fc0 sc0 lsf ws7">Mesma unidade de medida dos dados. </div><div class="t m0 x1 h7 y82 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h6 y83 ff3 fs3 fc1 sc0 lsf ws7">Interpretação </div><div class="t m0 x4 h7 y84 ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Quanto maior a medida, mais espalhados estão os dados, maior variab<span class="_0 blank"></span>ilidade </span></span></div><div class="t m0 x11 h7 y85 ff2 fs4 fc0 sc0 lsf ws7">da variável. </div><div class="t m0 x4 h7 y86 ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Atenção para unidades de medidas. </span></span></div><div class="t m0 x11 h7 y87 ff2 fs4 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h6 y88 ff3 fs3 fc1 sc0 lsf ws7">Propriedades </div><div class="t m0 x4 h7 y89 ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Nenhuma medida de dispersão pode ser negativa. Todas elas serão no míni<span class="_0 blank"></span>mo </span></span></div><div class="t m0 x11 h7 y8a ff2 fs4 fc0 sc0 lsf ws7">igual a 0. </div><div class="t m0 x4 h7 y8b ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Se somarmos um mesmo valor a cada uma das observações da variável, as </span></span></div><div class="t m0 x11 h7 y8c ff2 fs4 fc0 sc0 lsf ws7">medidas não mudam, continuam iguais. </div><div class="t m0 x4 h7 y8d ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Se multiplicarmos um mesmo valor a cada uma das observações da var<span class="_0 blank"></span>iável, as </span></span></div><div class="t m0 x11 h7 y8e ff2 fs4 fc0 sc0 lsf ws7">medidas são multiplicadas pelo módulo desse valor, com ex<span class="_0 blank"></span>ceção da variância, </div><div class="t m0 x11 h7 y8f ff2 fs4 fc0 sc0 lsf ws7">que é multiplicada pelo quadrado do valor. </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/95218c41-edd6-4b38-8de3-ad1fbdfa7fb8/bg6.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 lsf ws7">6 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="t m0 x1 h6 y90 ff3 fs3 fc1 sc0 lsf ws7">Coeficiente de variação </div><div class="t m0 x2f h9 y91 ff4 fs4 fc0 sc0 lsf ws11">\ue725\ue738 <span class="ws1 v6">(</span><span class="ls2a">\ue754<span class="lse v6">)</span><span class="ls2f">=</span></span><span class="v2">\ue74f</span></div><div class="t m0 x3a hd y92 ff4 fs4 fc0 sc0 lsf ws23">\ue754<span class="_0 blank"></span>\u0305 <span class="ff2 ws7 v3"> </span></div><div class="t m0 x4 h7 y93 ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Pode ser expresso como percentual. </span></span></div><div class="t m0 x4 h7 y94 ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Não tem unidade. </span></span></div><div class="t m0 x4 h7 y95 ff5 fs4 fc0 sc0 lsf ws22">\uf0b7<span class="ff6 ls2e ws7"> <span class="ff2 lsf">Pode ser usado para comparar a variabilidade de duas variáv<span class="_0 blank"></span>eis com unidades </span></span></div><div class="t m0 x11 h7 y96 ff2 fs4 fc0 sc0 lsf ws7">diferentes. </div><div class="t m0 x1 h2 y97 ff1 fs0 fc0 sc0 lsf ws7"> </div><div class="t m0 x1 h2 y98 ff1 fs0 fc0 sc0 lsf ws7"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
Compartilhar