Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Suatu sampel berukuran n = 10, memiliki variansi sampel 4,8 dan \(\bar x = 0,5\). Hitung \(\sum {({x^2})} \)!
- 5,08
- 45,7
- 48,2
- 68,2
- 25
PEMBAHASAN
\({S^2} = \frac{1}{{n – 1}}\sum\limits_{i = 1}^n {{{({x_i} – \bar x)}^2}} \) \(4,8 = \frac{1}{{10 – 1}}\sum\limits_{i = 1}^{10} {{{({x_i} – 0,5)}^2}} \) \(4,8(9) = \sum\limits_{i = 1}^{10} {({x_i}^2 – {x_i} + 0,25)} \) \(43,2 = \sum\limits_{i = 1}^{10} {{x_i}^2 – \sum\limits_{i = 1}^{10} {{x_i} + \sum\limits_{i = 1}^{10} {0,25} } } \) \(43,2 = \sum\limits_{i = 1}^{10} {{x_i}^2 – (n\bar x) + 10(0,25)} \) \(\sum\limits_{i = 1}^{10} {{x_i}^2 = 43,2 + 5 – 2,5} \) \(\sum\limits_{i = 1}^{10} {{x_i}^2 = } 45,7\)Jawaban pada pilihan: B. 45,7


