Chapter 4.6, Problem 9PPS

a

To determine

To write: The equation of the median fit line.

Answer to Problem 9PPS

The equation of the median fit line is $y=0.095x-94.3$ .

Explanation of Solution

Given information: refer to the table given above

Calculation:

Here, the data should be divided in three equal sections which in this case would be in the ratio of $2:1:2$ .

Now, let the Store Size be the x-coordinate and the Tubs be the y-coordinate.

Thus, the points for the median fit line are as follows,

	X-coordinate	Y-coordinate	X-Median	Y-Median
Section-1	(2100,2225)	(110,102)	2162	106
Section-2	3135	215	3135	215
Section-3	(3569,4587)	(312,265)	4078	2885

Thus, the slope of the Median-Fit Line is,

  $\begin{array}{l}m=\frac{y_3-y_1}{x_3-x_1}\\ m=\frac{288.5-106}{4078-2162}\\ m=0.095\mathrm{....}(1)\end{array}$

Therefore, the equation of the Median Fit Line using one point form is,

  $\begin{array}{c}y-y_1=m(x-x_1)\\ y-106=0.95(x-2162)\\ y=0.095x-94.3\end{array}$

b

To determine

To draw: The graph of the Median Fit Line and the points

Explanation of Solution

Graph:

  

The equation of the line is

  $y=0.095x-94.3$

c

To determine

To calculate: The number of tubs delivered to the store of size 1500 and 5000 (sq.ft.) respectively.

Answer to Problem 9PPS

The number of tubs delivered to the store of size 1500 and 5000 (sq.ft.) respectively are 48.2 and 380.7

Explanation of Solution

Given information: As derived in the previous part the equation of Median Fit Line is,

  $y=0.095x-94.3$ .

Calculation:

putting the values of x in equation we get,

  $\begin{array}{l}y=0.095\times 1500-94.3\\ y=48.2\end{array}$

And

  $\begin{array}{l}y=0.095\times 5000-94.3\\ y=380.7\end{array}$