Chapter 4.6, Problem 2CYU

To determine

To estimate the number of times caught stealing (CS) by a team that had 35 stolen bases (SB).

Answer to Problem 2CYU

The estimated number of caught stealing is $16.286$ .

Explanation of Solution

Concept used: Linear interpolation is used to estimate the unknown value between two known coordinates by connecting them into a straight line. The value of the unknown interpolant is estimated using the equation of slopes.

Formula used: $\frac{\mathrm{y}-{\mathrm{y}}_0}{\mathrm{x}-{\mathrm{x}}_0}=\frac{{\mathrm{y}}_1-{\mathrm{y}}_0}{{\mathrm{x}}_1-{\mathrm{x}}_0}$

Calculation:

The two known coordinates adjacent to the unknown value to be estimated are $(31,14)$ and $(45,22)$ .

Therefore, The coordinate which we have to estimate is $(35,\mathrm{y})$ .

Thus, the expression will be,

  $\begin{array}{c}\frac{\mathrm{y}-14}{35-31}=\frac{22-14}{45-31}\\ \frac{\mathrm{y}-14}{4}=\frac{8}{14}\\ \mathrm{y}=\frac{32}{14}+14\\ \mathrm{y}=16.286\text{}\end{array}$