Contoh Soal 7 Statistika

$\begin{array}{ll}\\ 31.&(\textbf{SMBB TELKOM 06})\\ &\textrm{Berikut tidak termasuk ukuran penyebaran}\\ &\textrm{data adalah}\: ....\\ &\begin{array}{ll}\\ \textrm{a}.&\textrm{rentang}\\ \textrm{b}.&\textrm{varians}\\ \textrm{c}.&\textrm{jarak antar kuartil}\\ \color{red}\textrm{d}.&\textrm{kuartil}\\ \textrm{e}.&\textrm{simpangan baku} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}&\textrm{Ingat bahwa mean, median, modus}\\ &\color{red}\textrm{adalah bagian ukuran pemusatan data}\\ &\textrm{sedangkan kuartil adalah ukuran letak data} \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 32.&\textrm{Perhatikanlah barisan}\: \: 1,-2,3,-4,5,-6,...\\ &\textrm{dengan suku ke}-n\: \: \textrm{adalah}\: \: (-1)^{n-1}\times n.\\ &\textrm{Rata-rata 200 suku pertama barisan tersebut}\\ &\textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&-1\\ \color{red}\textrm{b}.&-0,5\\ \textrm{c}.&0\\ \textrm{d}.&0,5\\ \textrm{e}.&1 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}&\textrm{Diketahui bahwa}\: : 1,-2,3,-4,5,-6,...,199,-200\\ &\overline{x}_{\color{red}200}=\displaystyle \frac{1-2+3-4+5-6+...+199-200}{200}\\ &\: \: \: \quad =\displaystyle \frac{-100}{200}=-0,5 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 33.&(\textbf{STT TELKOM 2005})\\ &\textrm{Seratus mahasiswa telah mengikuti ujian psikotes}\\ &\textrm{dan rata-rata skornya yang diperoleh adalah 100}.\\ &\textrm{Banyaknya mahasiswa junior yang mengikuti}\\ &\textrm{ujian psikotes}\: \: 50\%\: \: \textrm{lebih besar dari banyknya ma}-\\ &\textrm{hasiswa senior. Jika rata-rata skor dari mahasiswa}\\ &\textrm{senior}\: \: 50\%\: \: \textrm{lebih tinggi dari mahasiswa junior,}\\ &\textrm{maka rata-rata skor mahasiswa senior adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&110\\ \textrm{b}.&115\\ \textrm{c}.&120\\ \color{red}\textrm{d}.&125\\ \textrm{e}.&150 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}&\textrm{Perhatikanlah tabel berikut}\\ &\begin{array}{|c|c|c|}\hline \textrm{Mahasiswa}&\textrm{Mahasiswa}&\color{purple}\textrm{Total}\\ \textrm{senior}&\textrm{junior}&\\\hline n_{\color{red}senior}&n_{\color{red}junior}&\color{black}100\\\hline n_{\color{red}s}&\displaystyle \frac{3}{2}n_{\color{red}s}&\color{black}100\\\hline \overline{x}_{\color{red}senior}&\overline{x}_{\color{red}junior}&\color{red}100\\\hline \overline{x}_{\color{red}s}&\displaystyle \frac{2}{3}\overline{x}_{\color{red}s}&\color{red}100\\\hline \end{array}\\ &n_{\color{red}s}+\displaystyle \frac{3}{2}n_{\color{red}s}=\color{black}100\\ &\: \: \: \: \qquad n_{\color{red}s}=\color{black}40,\\ &\textrm{maka}\: \: n_{\color{red}j}=\color{black}60.\\ &\textrm{Selanjutnya kita tentukan nilai rata-rata}\\ &\textrm{mahasiswa senior, dengan}\\ &\displaystyle \frac{\color{black}40\color{blue}\overline{x}_{\color{red}s}+\color{black}(60)\color{blue}\displaystyle \frac{2}{3}\overline{x}_{\color{red}s}}{\color{black}100}=\color{red}100\\ &\: \: \: \, \quad\quad\qquad\color{black}80\color{blue}\overline{x}_{\color{red}s}=10000\\ &\qquad\qquad\qquad \color{blue}\overline{x}_{\color{red}s}=\displaystyle \frac{10000}{\color{black}80}\\ &\qquad\qquad\qquad \color{blue}\overline{x}_{\color{red}s}=\color{red}125 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 34.&(\textbf{SPMB 04})\\ &\textrm{Median, rata-rata, dan modus dari data yang}\\ &\textrm{terdiri atas empat bilangan asli adalah 7. Jika}\\ &\textrm{selisih antara data terbesar dan terkecil adalah}\\ &\textrm{6, maka hasil kali keempat datum tersebut}\\ &\textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&1.864\\ \textrm{b}.&1.932\\ \color{red}\textrm{c}.&1.960\\ \textrm{d}.&1.976\\ \textrm{e}.&1.983 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}&\textrm{Diketahui bahwa}\: :x_{1},x_{2},x_{3},\: \: \textrm{dan}\: \: x_{4}\: \: \textrm{adalah}\\ &\textrm{asli dengan}\: \: x_{4}-x_{1}=6\: ........\color{red}(1)\\ &\&\: \textrm{modusnya adalah 7, maka data dapat dituliskan}\\ &:\: x_{1},\color{red}7,7\color{blue},x_{4}.\: \: \textrm{Jawaban ini sesuai karena median} = \color{red}7.\\ &\textrm{Karena mean}\: =7,\: \: \textrm{maka dapat dituliskan}\\ &\displaystyle \frac{x_{1}+x_{2}+x_{3}+x_{4}}{4}=7\Leftrightarrow x_{1}+x_{2}+x_{3}+x_{4}=28\\ &\Leftrightarrow x_{1}+14+x_{4}=28\Leftrightarrow x_{4}+x_{1}=14\: ........\color{red}(2)\\ &\color{black}\textrm{Selanjutnya kita eliminasi}\: \: \color{blue}(1)\&(2)\\ &\color{blue}\begin{array}{llll}\\ x_{4}-x_{1}&=6&\\ x_{4}+x_{1}&=14\: \: \: +\\\hline 2x_{4}\: \: \qquad&=20&\\ x_{4}&=10\: .......\color{red}(3)\\ \textrm{maka}\: \: x_{1}&=4\: .........\color{red}(4) \end{array}\\ &\textrm{Jadi},\: \: x_{1}\times x_{2}\times x_{3}\times x_{4}=(4).(7).(7).(10)=\color{red}1960 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 35.&\textrm{Desil ke-8}\: \: \left ( D_{8} \right )\: \: \textrm{dari data berikut adalah}\: ....\\ &\begin{array}{|c|c|}\hline \textrm{Nilai}&f\\\hline 41-45&7\\ 46-50&12\\ 51-55&9\\ 56-60&8\\ 61-65&4\\\hline \end{array}\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&58\\ \textrm{b}.&57,5\\ \textrm{c}.&57\\ \textrm{d}.&56,75\\ \textrm{e}.&56,25 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\color{blue}\begin{aligned}\textrm{Diketahui}&\: \textrm{desil ke}-8=\color{black}D_{8},\: \: \textrm{dengan}\: \: n=\sum f=40\\ D_{i}&=t_{b}+p\left ( \displaystyle \frac{\displaystyle \frac{i\times n}{10}-F}{f} \right )\\ D_{8}&= \textrm{datum ke}-\left ( \displaystyle \frac{8n}{10} \right )=x_{\frac{8\times 40}{10}}=\color{red}x_{32}\\ \textrm{Dan}\: \: \color{red}x_{32}\: \: &\textrm{terletak di kelas interval}\: :\: \color{red}56-60 \\ D_{8}&=55,5+5\left ( \displaystyle \frac{32-28}{8} \right )\\ &=55,5+2,5\\ &=\color{red}58 \end{aligned} \end{array}$