Chapter 1.6, Problem 11PPS

a.

To determine

To graph: The scatter plot between the different months and average temperature for Louisville, Kentucky.

Explanation of Solution

Given information:

The data is provided below.

  $\begin{array}{cc}\text{Month}& \text{Temperature }\left(°F\right)\\ \text{January}& 41\\ \text{February}& 47\\ \text{March}& 57\\ \text{April}& 67\\ \text{May}& 75\\ \text{June}& 83\\ \text{July}& 87\\ \text{August}& 86\\ \text{September}& 79\\ \text{October}& 68\\ \text{November}& 56\\ \text{December}& 45\end{array}$

Graph:

When the relationship between two data sets is to be analyzed scatter plot is used.

Provided two data sets month and average temperature during that month. The data is provided below.

  $\begin{array}{cc}\text{Month}& \text{Temperature }\left(°F\right)\\ \text{January}& 41\\ \text{February}& 47\\ \text{March}& 57\\ \text{April}& 67\\ \text{May}& 75\\ \text{June}& 83\\ \text{July}& 87\\ \text{August}& 86\\ \text{September}& 79\\ \text{October}& 68\\ \text{November}& 56\\ \text{December}& 45\end{array}$

On the x -axis of coordinate plane denote the month from 1 to 12 as data is from January to December.

On y -axis plot the average temperature in $\left(°F\right)$ .

The scatter plot of the data is provided below,

  

Interpretation:

It is observed that first the temperature increases till month of July and then it starts to decrease gradually that is there is a strong nonlinear relationship between x and y .

b.

To determine

To describe: The scatter plot between the different months and average temperature for Louisville, Kentucky.

Answer to Problem 11PPS

The scatter plot between the month and average temperature shows a strong nonlinear relationship.

Explanation of Solution

Given information:

The data is provided below.

  $\begin{array}{cc}\text{Month}& \text{Temperature }\left(°F\right)\\ \text{January}& 41\\ \text{February}& 47\\ \text{March}& 57\\ \text{April}& 67\\ \text{May}& 75\\ \text{June}& 83\\ \text{July}& 87\\ \text{August}& 86\\ \text{September}& 79\\ \text{October}& 68\\ \text{November}& 56\\ \text{December}& 45\end{array}$

When the relationship between two data sets is to be analyzed scatter plot is used.

Provided two data sets,

  $\begin{array}{cc}\text{Month}& \text{Temperature }\left(°F\right)\\ \text{January}& 41\\ \text{February}& 47\\ \text{March}& 57\\ \text{April}& 67\\ \text{May}& 75\\ \text{June}& 83\\ \text{July}& 87\\ \text{August}& 86\\ \text{September}& 79\\ \text{October}& 68\\ \text{November}& 56\\ \text{December}& 45\end{array}$

Initially the temperature rises from 41 to 987 degree Fahrenheit till month of July so till here the relationship is positive after the month of July the temperature falls to 45 degrees Fahrenheit in December depicting a negative relationship. So, it can be said that the data portrays a strong nonlinear relationship.

Thus, the scatter plot between the month and average temperature shows a strong nonlinear relationship.