ข้อสอบคณิต O-NET - 2550

$$\begin{gathered} \mathrm{จากสูตร} \mathrm{ความแปรปรวน} \\ s = \frac{\sum {\left(x_i-\overline{x}\right)}^2}{N} = \frac{\sum {x_i}^2}{N}- {\overline{x}}^2 \\ \mathrm{จากโจทย์} \end{gathered}$$

$$\begin{gathered} \begin{array}{ccccc}& & 10 \mathrm{คน}& & \end{array} \begin{array}{ccccc} & & 20 \mathrm{คน}& & \end{array} \\ \overbrace{\begin{array}{ccccc}10,& 10,& 10,& \dots ,& 10\end{array}} \overbrace{ \begin{array}{ccccc}8.5,& 8.5,& 8.5,& \dots ,& 8.5\end{array}} \\ {x}_i : 12, 12, 12, \dots , 12 10.5, 10.5, 10.5, \dots , 10.5 \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} \overline{x} = \frac{\left(12\times 10\right)+\left(10.5\times 20\right)}{30} \\ = \frac{330}{30} = 11 \\ x_i-11 : 1, 1, 1, \dots , 1 -0.5, -0.5, -0.5, \dots , -0.5 \\ {\left(x_i-11\right)}^2 : 1, 1, 1, \dots , 1 0.25, 0.25, 0.25, \dots , 0.25 \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} \mathrm{ความแปรปรวน} = \frac{\left(1\times 10\right)+\left(0.25\times 20\right)}{30} \\ = \frac{15}{30} \\ = \frac{1}{2} \end{gathered}$$