Chapter 14.1, Problem 6CFU

a.

To determine

To find the range of the data.

Answer to Problem 6CFU

  $27$ .

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

Maximum value from the data is $69$ , and the minimum value from the data is $42$

Therefore the range of the above data is $69-42=27$ .

b.

To determine

To find the appropriate interval.

Answer to Problem 6CFU

  $40-45,45-50,50-55,55-60,60-65,65-70$ .

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

Since the data ranges from $69$ to $42$ , the appropriate class interval be $5$ , starting with $40$ points and ending with $70$ points, hence the classes are

  $40-45,45-50,50-55,55-60,60-65,65-70$

c.

To determine

To find the class limits of each class.

Answer to Problem 6CFU

  $40,45,50,55,,60,65,70$ .

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

The class limits of the above classes are upper and lower limits of each class they are

  $40,45,50,55,,60,65,70$

d.

To determine

To find the class marks of the classes.

Answer to Problem 6CFU

  $42.5,47.5,52.5,57.5,62.5,67.5$ .

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

The class mark of each class is the average of the upper and lower limit; this is called mid value also

Hence the class marks of the classes $40-45,45-50,50-55,55-60,60-65,65-70$ are $42.5,47.5,52.5,57.5,62.5,67.5$ respectively

e.

To determine

To make a table listing class limits

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

Make a table listing class limits; Use the tallies to determine the number of scores in each interval

  

f.

To determine

To draw the histogram of the data.

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

Label the horizontal axis with the class limits. The vertical axis should be labeled from 0 to a value that will allow for the bars side by side so that the height of the bar corresponds to its interval’s frequency

The histogram of the above data is as below

  

g.

To determine

To name the intervals that describe the age of most presidents.

Answer to Problem 6CFU

  $50-55,55-60$ .

Explanation of Solution

Given:

The data which gives the ages of the first $42$ presidents when they first took office

  $\begin{array}{l}57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,50,\\ 47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46\end{array}$

Calculation:

There are 12 presidents are belongs to each of the classes $50-55,55-60$ .