Bab 7 Statistik

Posted on May 31, 2016 by user

7.3 Statistik, SPM Praktis (Kertas 1)

Soalan 1:

Sisihan piawai bagi lima nombor ialah 6 dan hasil tambah bagi kuasa dua nombor-nombor itu ialah 260. Cari min bagi set nombor itu.

Penyelesaian:

$\begin{array}{l} Diberi σ = 6, Σ x^{2} = 260. \\ σ = 6 \\ \sqrt{\frac{Σ x^{2}}{n} - {\bar{X}}^{2}} = 6 \\ \frac{Σ x^{2}}{n} - {\bar{X}}^{2} = 36 \\ \frac{260}{5} - {\bar{X}}^{2} = 36 \\ {\bar{X}}^{2} = 16 \\ \bar{X} = \pm 4 \\ ∴ min = \pm 4 \end{array}$

Soalan 2:

Kedua-dua min dan sisihan piawai bagi set nombor 1, 3, 7, 15, m dan n ialah 6. Cari

(a) nilai m+ n,

(b) nilai yang mungkin bagi n.

Penyelesaian:

(a)

$\begin{array}{l} Diberi min = 6 \\ \frac{Σ x}{n} = 6 \\ \frac{Σ x}{6} = 6 \end{array}$

1 + 3 + 7 + 15 + m + n= 36

26 + m + n = 36

m + n = 10

(b)

$\begin{array}{l} σ = 6 \\ σ^{2} = 36 \\ \frac{Σ x^{2}}{n} - {\bar{X}}^{2} = 36 \\ \frac{1 + 9 + 49 + 225 + m^{2} + n^{2}}{6} - 6^{2} = 36 \\ \frac{284 + m^{2} + n^{2}}{6} - 36 = 36 \\ \frac{284 + m^{2} + n^{2}}{6} = 72 \end{array}$

284 + m² + n² = 432

m² + n² = 148

Daripada (a), m = 10 – n

(10 – n)² + n² = 148

100 – 20n + n²+ n² = 148

2n² – 20n – 48 = 0

n² – 10n – 24 = 0

(n – 6)(n + 4) = 0

n = 6 atau n = –4