ข้อสอบ PAT 1 - ตุลาคม 2559

$$\begin{gathered} \mathrm{จากโจทย์}\hspace{0.17em}\sum _{\mathrm{i}=1}^5({\mathrm{x}}_{\mathrm{i}}+{\mathrm{y}}_{\mathrm{i}})=275 \mathrm{จะได้} \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}+\sum _{\mathrm{i}=1}^5{\mathrm{y}}_{\mathrm{i}}=275\to \boxed{1} \\ \sum _{\mathrm{i}=1}^5(20{\mathrm{x}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}})=250 \mathrm{จะได้} 20\sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}-\sum _{\mathrm{i}=1}^5{\mathrm{y}}_{\mathrm{i}}=250\to \boxed{2} \\ \mathrm{นำ} \boxed{1}+\boxed{2} \mathrm{จะได้} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}21\sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}=525 \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}=25 ; \mathrm{แทนใน} \boxed{1} \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} 25+\sum _{\mathrm{i}=1}^5{\mathrm{y}}_{\mathrm{i}}=275 \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \sum _{\mathrm{i}=1}^5{\mathrm{y}}_{\mathrm{i}}=250 \\ \mathrm{จากโจทย์}+\mathrm{ที่คำนวณ} \mathrm{จะได้} \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}^2=175 , \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}{\mathrm{y}}_{\mathrm{i}}=1575 , \\ \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}=25 \mathrm{และ} \sum _{\mathrm{i}=1}^5{\mathrm{y}}_{\mathrm{i}}=250 \\ \mathrm{จากโจทย์} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{y}=\mathrm{mx}+\mathrm{c}\to \boxed{\mathrm{a}} \end{gathered}$$

$$\begin{gathered} \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}=\mathrm{m}\sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}+\sum _{\mathrm{i}=1}^5\mathrm{c} \mathrm{จะได้} 250=25\mathrm{m}+5\mathrm{c} \\ 50=5\mathrm{m}+\mathrm{c}\to \boxed{3} \\ \sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}{\mathrm{y}}_{\mathrm{i}}=\mathrm{m}\sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}}^2+\mathrm{c}\sum _{\mathrm{i}=1}^5{\mathrm{x}}_{\mathrm{i}} \mathrm{จะได้} 1575=175\mathrm{m}+25\mathrm{c} \\ 63=7\mathrm{m}+\mathrm{c}\to \boxed{4} \\ -\mathrm{จาก} \boxed{3}, \boxed{4} \mathrm{แก้} 2 \mathrm{สมการ} 2 \mathrm{ตัวแปร} \\ \mathrm{จะได้}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \mathrm{m}=6.5 , \mathrm{c}=17.5 \end{gathered}$$

$$\begin{gathered} \mathrm{จาก} \boxed{\mathrm{a}} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{y}=\mathrm{mx}+\mathrm{c} \\ \mathrm{จะได้} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{y}=6.5\mathrm{x}+17.5 \\ \mathrm{ถ้า} \mathrm{x}=4 \mathrm{จะได้} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{y}=6.5\left(4\right)+17.5 \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \mathrm{y}=43.5 \\ \mathrm{ดังนั้น} \mathrm{ค่าประมาณของ} \mathrm{y} \mathrm{เท่ากับ} 43.5 \end{gathered}$$