Contoh Soal 10 Statistika

Soal sebelumnya (yaitu Contoh Soal 9 Statistika) klik di sini

$\begin{array}{ll} 41.&\textrm{Median dan modus dari data berikut}\\ &\color{red}3,6,7,8,4,5,9,6\\ &\textrm{ adalah}\: ....\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{7 dan 5}&&&\textrm{d}.&\textrm{5 dan 6}\frac{1}{2}\\ \textrm{b}.&\textrm{6 dan 6} &\textrm{c}.&\textrm{6 dan 7}&\textrm{e}.&\textrm{5 dan 6} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{b}\\ &\begin{aligned}&\textrm{Diketahui}\: \: \color{blue} n=8\\ &\textrm{Datum diurutkan dari kecil ke besar}\\ &:3,4,5,\color{red}6,6\color{black},7,8,9\\ &\bullet \: \: \textbf{modus} =M_{o}=6,\\ &\bullet \: \: \textbf{mean} =\overline{x}=6 \end{aligned} \end{array}$.

$\begin{array}{ll} 42.&\textrm{Hasil tes matematika di suatu kelas yang}\\ &\textrm{diikuti tes 49 siswa menghasilkan nilai}\\ &\textrm{rata-rata 7}.\: \textrm{Jika Andi ikut tes susulan}\\ &7,04.\: \textrm{Nilai Andi adalah}\: ....\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{7,5}&&&\textrm{d}.&\textrm{9}\\ \textrm{b}.&\textrm{8} &\textrm{c}.&\textrm{8,5}&\textrm{e}.&\textrm{9,5} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned}\textrm{Misalkan}&\: \: \color{red}y\color{black}=\textrm{besar nilai Andi}\\ \overline{x}_{gabungan}&=\displaystyle \frac{n.\overline{x}+\color{red}y}{n+1}\\ 7,04&=\displaystyle \frac{49\times 7+\color{red}y}{49+1}\\ 7,04&=\displaystyle \frac{343+\color{red}y}{50}\\ 343+\color{red}y&=50\times \left ( 7,04 \right )\\ 343+\color{red}y&=352\\ y&=352-343\\ &=\color{red}9 \end{aligned} \end{array}$.

$\begin{array}{ll} 43.&\textrm{Mean dari tabel berikut adalah}\: ....\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 50-54&4\\ 55-59&6\\ 60-64&10\\\hline \end{array}\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{60,5}&&&\textrm{d}.&\textrm{58,5}\\ \textrm{b}.&\textrm{60} &\textrm{c}.&\textrm{59,5}&\textrm{e}.&\textrm{57} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{d}\\ &\begin{aligned}&\begin{array}{|c|c|c|c|c|}\hline \textrm{Ukuran}&x_{i}&d_{i}=x_{i}-x_{s}&f_{i}&f_{i}\times d_{i}\\\hline 50-54&52&-10&4&-40\\\hline 55-59&57&-5&6&-30\\\hline 60-64&62&0&10&0\\\hline \textrm{Jumlah}&&&20&-70\\\hline \end{array}\\ &\overline{x}=x_{s}+\displaystyle \frac{\displaystyle \sum_{i=1}^{n}f_{i}\times d_{1}}{\displaystyle \sum_{i=0}^{n}f_{i}}=62+\displaystyle \frac{-70}{20}\\ &\: \: =62-3,5=\color{red}58,5 \end{aligned} \end{array}$.

$\begin{array}{ll} 44.&\textrm{Median dari tabel berikut adalah}\: ....\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 47-49&1\\ 50-52&6\\ 53-55&6\\ 56-58&7\\ 59-61&4\\\hline \end{array}\\ &\begin{array}{lllllll} \textrm{a}.&\textrm{55,5}&&&\textrm{d}.&\textrm{53,5}\\ \textrm{b}.&\textrm{55} &\textrm{c}.&\textrm{54,5}&\textrm{e}.&\textrm{53} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{b}\\ &\begin{aligned}&\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 47-49&\color{red}1\\ 50-52&\color{red}6\\ \color{blue}53-55&\color{blue}6\\ 56-58&7\\ 59-61&4\\\hline &24\\\hline \end{array}\\ &\textrm{Median posisi datumnya}:\\ &\textrm{datum ke}-\left ( \displaystyle \frac{24}{2} \right )=x_{._{12}}\\ &\textrm{dan terletak di interval}\\ &53-55,\: \: \textrm{dengan}\: \: f_{k}=1+6=7\\ &\textrm{serta}\: \: c=3\\ &M_{e}=Q_{2}=L_{i}+c\left ( \displaystyle \frac{\displaystyle \frac{n}{2}-f_{k}}{f} \right )\\ &M_{e}=Q_{2}=52,2+3\left ( \displaystyle \frac{\displaystyle \frac{24}{2}-7}{6} \right )\\ &\: \quad=52,5+3\left ( \displaystyle \frac{12-7}{6} \right )\\ &\: \quad=52,5+\left ( \displaystyle \frac{5}{2} \right )\\ &\: \quad=52,5+2,5\\ &\: \quad=\color{red}55 \end{aligned} \end{array}$.

$\begin{array}{ll} 45.&\textrm{Modus dari tabel berikut adalah}\: ....\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 50-54&4\\ 55-59&6\\ 60-64&8\\ 65-69&16\\ 70-74&10\\ 75-79&4\\ 80-84&2\\\hline \end{array}\\ &\begin{array}{lllllll}\\ \textrm{a}.&\textrm{67,32}&&&\textrm{d}.&\textrm{70,12}\\ \textrm{b}.&\textrm{67,36} &\textrm{c}.&\textrm{67,56}&\textrm{e}.&\textrm{70,36} \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textrm{b}\\ &\begin{aligned} &\textrm{Perhatikan tabelnya lagi}\\ &\textrm{dengan penambahan warna berikut ini}\\ &\begin{array}{|c|c|}\hline \textrm{Ukuran}&\textrm{Frekuensi}\\\hline 50-54&4\\ 55-59&6\\ 60-64&\color{red}8\\ \color{blue}65-69&\color{blue}16\\ 70-74&\color{red}10\\ 75-79&4\\ 80-84&2\\\hline \end{array}\\ &\textrm{Diketahui}\: n=\color{blue}50\\ &\textrm{modus terletak pada kelas}\\ &\textrm{interval dengan frekuensi}\\ &\textrm{terbesar, yaitu}:16.\: \textrm{Kelas intervalnya}\\ &65-69,\: \: \textrm{dengan}\: \: c=5\\ &\textrm{serta}\: \: \begin{cases} \triangle _{1} & =f-f_{1}=16-8=8 \\ \triangle _{2} & =f-f_{2}=16-10=6 \end{cases}\\ &M_{o}=L+c\left ( \displaystyle \frac{\triangle _{1}}{\triangle _{1}+\triangle _{2}} \right )\\ &\quad\: \: =64,5+5\left ( \displaystyle \frac{8}{8+6} \right )\\ &\quad\: \: =64,5+\displaystyle \frac{40}{14}\\ &\quad\: \: =64,5+2,857\\ &\quad\: \: =\color{red}67,36 \end{aligned} \end{array}$.