Chapter 4.4, Problem 22E

To determine

To write: Possible coordinates for missing data points in the given scatter plot.

Answer to Problem 22E

Four possible missing points are $(12,98.88),(14,112.41),(16,125.94)$ and $(18,139.47)$ .

Explanation of Solution

Given information: A scatter plot with some missing data points is given.

Calculation:

Using the first and last point on the scatter plot, i.e. $(3,38)$ and $(20,153)$ to derive the equation by utilizing point-slope formula,

  $y-y_1=m(x-x_1)$

where, $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}=\frac{153-38}{20-3}\\ =\frac{115}{17}\end{array}$

Substituting the values derived so far in slope-intercept form,

  $y-38=\frac{115}{17}(x-3)$

Putting $x=12,14,16$ and $18$ in the above stated equation to get different values of $y$ and arranging those values in a table,

  $\begin{array}{lllll}x\hfill & 12\hfill & 14\hfill & 16\hfill & 18\hfill \\ y\hfill & 98.88\hfill & 112.41\hfill & 125.94\hfill & 139.47\hfill \end{array}$

Thus, the four possible missing points are shown in the table.