Question

A college professor collected data on the number of absences and the final grades of seven students from his statistics class. The data is shown in the table and graph below.Based on the scatterplot, which is the best prediction of the final grade of a student with 10 absences?

Answer 1

Answer:

The best prediction for the final grade of a student with 10 absences = 68.67

Explanations:

By proper observation of the table, 10 absences will fall between 9 and 12 absences.

Let x represent the number of absences

y represent the final grades of students

`\begin{gathered} x_0\text{ = 9} \\ x_1\text{ = 12} \\ y_0\text{ = 74} \\ y_1\text{ = 58} \\ x\text{ = 10} \\ y\text{ = ?} \end{gathered}`

Using the extrapolation formula:

`\begin{gathered} (y-y_0)/(y_1-y_0)=\text{ }(x-x_0)/(x_1-x_0) \\ (y-74)/(58-74)=\text{ }(10-9)/(12-9) \\ (y-74)/(-16)=\text{ }(1)/(3) \\ 3(y-74)\text{ = -16(1)} \\ 3y\text{ - }222\text{ = -16} \\ 3y\text{ = -16 + 222} \\ 3y\text{ = }206 \\ y\text{ = }(206)/(3) \\ y\text{ = }68.67 \end{gathered}`