7.3.4 Statistik, SPM Praktis (Kertas 1)

Soalan 7:
Satu set data mengandungi dua belas nombor positif.
$\text{Diberi bahawa }\Sigma {\left(x-\overline{x}\right)}^2=600\text{ dan }\Sigma x^2=1032.$
Cari
(a) varians
(b) min

Penyelesaian:
(a)
$\begin{array}{l}\text{Varians}=\frac{\Sigma {\left(x-\overline{x}\right)}^2}{N}\\ =\frac{600}{12}\\ =50\end{array}$

(b)
$\begin{array}{l}\text{Varians}=\frac{\Sigma x^2}{N}-{\left(\overline{x}\right)}^2\\ 50=\frac{1032}{12}-{\left(\overline{x}\right)}^2\\ {\left(\overline{x}\right)}^2=86-50\\ =36\\ \overline{x}=36\end{array}$