Chapter 14.3, Problem 29E

a.

To determine

To calculate: The range of the number of programs sold.

Answer to Problem 29E

The range is $45.$

Explanation of Solution

Given information:

Twelve students are selling programs at the Grove City High School to raise money for the athletic department. The numbers of programs sold by each student are

$51,27,55,54,68,60,39,46,46,53,57,23.$

Formula used:

The range of a set of data is the difference between the greatest and the least values in the set.

Calculation:

Consider the data in ascending order ,

  $\{23,27,39,46,46,51,53,54,55,57,60,68\}.$

So, $n=12$ .

The greatest value in the set is $68.$

The least value in the set is $23.$

The range is −

  $\begin{array}{l}=68-23\\ =45.\end{array}$

Hence, the range is $45.$

b.

To determine

To calculate: The class interval.

Answer to Problem 29E

The class interval is 10 points.

Explanation of Solution

Given information:

Twelve students are selling programs at the Grove City High School to raise money for the athletic department. The numbers of programs sold by each student are

$51,27,55,54,68,60,39,46,46,53,57,23.$

Formula used:

The class interval is the range of each class.

Calculation:

Consider the data in ascending order ,

  $\{23,27,39,46,46,51,53,54,55,57,60,68\}.$

So, $n=12$ .

An appropriate class interval is 10 points, beginning with 20 points and ending with 70 points. There will be five classes.

Hence, the class interval is 10 points.

c.

To determine

To calculate: The class limits.

Answer to Problem 29E

The class limits are 20, 30, 40, 50, 60, and 70.

Explanation of Solution

Given information:

Twelve students are selling programs at the Grove City High School to raise money for the athletic department. The numbers of programs sold by each student are

$51,27,55,54,68,60,39,46,46,53,57,23.$

Formula used:

The class limits of a set of data organized in a frequency distribution are the upper and lower values in each interval .

Calculation:

Consider the data in ascending order ,

  $\{23,27,39,46,46,51,53,54,55,57,60,68\}.$

So, $n=12$ .

An appropriate class interval is 10 points, beginning with 20 points and ending with 70 points. There will be five classes.

The class limits are 20, 30, 40, 50, 60, and 70.

Hence, the class limits are 20, 30, 40, 50, 60, and 70.

d.

To determine

To construct: The frequency distribution of the data.

Answer to Problem 29E

Class Intervals	Tallies	Frequency
$20-30$	$\left|\right|$	2
$30-40$	$|$	1
$40-50$	$\text{||}$$$	2
$50-60$	$\bcancel{\left|\right|\left|\right|}$	5
$60-70$	$\text{||}$	2

Explanation of Solution

Given information:

Twelve students are selling programs at the Grove City High School to raise money for the athletic department. The numbers of programs sold by each student are

$51,27,55,54,68,60,39,46,46,53,57,23.$

Formula used:

The class limits of a set of data organized in a frequency distribution are the upper and lower values in each interval .

Calculation:

Consider the data in ascending order ,

  $\{23,27,39,46,46,51,53,54,55,57,60,68\}.$

So, $n=12$ .

An appropriate class interval is 10 points, beginning with 20 points and ending with 70 points. There will be five classes.

The class limits are 20, 30, 40, 50, 60, and 70.

Class Intervals	Tallies	Frequency
$20-30$	$\left|\right|$	2
$30-40$	$|$	1
$40-50$	$\text{||}$$$	2
$50-60$	$\bcancel{\left|\right|\left|\right|}$	5
$60-70$	$\text{||}$	2

Hence, the above table ids the frequency distribution of the data.

e

To determine

To sketch: The histogram of the data.

Explanation of Solution

Given information:

Twelve students are selling programs at the Grove City High School to raise money for the athletic department. The numbers of programs sold by each student are

$51,27,55,54,68,60,39,46,46,53,57,23.$

Graph:

  

Figure 1.

Interpretation:

The graph represent the number of programs sold by each student. The maximum score is 68 and the minimum score is 23. The interval size is 10.