Beginning Statistics, 2nd Edition
Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
Question
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Chapter 2.1, Problem 8E

(a)

To determine

To find:

The class width for the given frequency distribution.

(a)

Expert Solution
Check Mark

Answer to Problem 8E

Solution:

The class width of the given frequency distribution is 0.99 which is approximately equal to 1.0.

Explanation of Solution

Given:

The table is given as,

Hourly Wages of Surveillance
Operators (in Dollars)
Class Frequency
10.5011.49 92
11.5012.49 78
12.5013.49 68
13.5014.49 45
14.5015.49 34

The upper limit of the distribution is given as 15.49 and the lower limit is given as 10.50. The number of classes is 5.

Formula used:

The formula to calculate the class width is,

Classwidth=UpperlimitLowerlimitNumberofclass

Calculation:

The smallest number that can belong to a particular class is termed as lower class limit and the largest number that can belong to a particular class is termed as upper class limit.

Substitute 15.49 for upper limit and 10.50 for lower limit and 5 for the number of classes in the formula,

Classwidth=15.4910.505=4.995=0.9981.0

(b)

To determine

To find:

The class boundary for each class of the given frequency distribution.

(b)

Expert Solution
Check Mark

Answer to Problem 8E

Solution:

The class boundary for each class of the given frequency distribution is,

Class Frequency Class boundaries
10.5011.49 92 10.49511.495
11.5012.49 78 11.49512.495
12.5013.49 68 12.49513.495
13.5014.49 45 13.49514.495
14.5015.49 34 14.49515.495

Explanation of Solution

Given:

The table is given as,

Hourly Wages of Surveillance
Operators (in Dollars)
Class Frequency
10.5011.49 92
11.5012.49 78
12.5013.49 68
13.5014.49 45
14.5015.49 34

Formula used:

The formula to calculate the class boundary is,

Classboundary=Upperlimitofoneclass+Lowerlimitofnextclass2

Calculation:

It is known that the smallest number that can belong to a particular class is termed as lower class limit and the largest number that can belong to a particular class is termed as upper class limit.

For the first class, since, the largest number is 11.49 and 11.50 is the smallest number in the next class, then, substitute 11.49 for upper limit and 11.50 for lower limit in the formula,

Classboundary=11.49+11.502=22.992=11.495

Continuing the same way, the class boundaries of all the five classes are shown in the table given below,

Table 1

Class Frequency Class boundaries
10.5011.49 92 10.49511.495
11.5012.49 78 11.49512.495
12.5013.49 68 12.49513.495
13.5014.49 45 13.49514.495
14.5015.49 34 14.49515.495

(c)

To determine

To find:

The midpoint of each class for the given frequency distribution.

(c)

Expert Solution
Check Mark

Answer to Problem 8E

Solution:

The midpoint of each class for the given frequency distribution is,

Class Frequency Class boundaries Midpoint
10.5011.49 92 10.49511.495 10.995
11.5012.49 78 11.49512.495 11.995
12.5013.49 68 12.49513.495 12.995
13.5014.49 45 13.49514.495 13.995
14.5015.49 34 14.49515.495 14.995

Explanation of Solution

Given:

The table is given as,

Hourly Wages of Surveillance
Operators (in Dollars)
Class Frequency
10.5011.49 92
11.5012.49 78
12.5013.49 68
13.5014.49 45
14.5015.49 34

Formula used:

The formula to calculate the midpoint of any class is,

Midpoint=Upperlimit+Lowerlimit2

Calculation:

The smallest number that can belong to a particular class is termed as lower class limit and the largest number that can belong to a particular class is termed as upper class limit.

For the first class,

Substitute 11.49 for upper limit and 10.50 for lower limit in the formula,

Midpoint=11.49+10.502=21.992=10.995

Continuing the same way, the midpoint of all the five classes are shown in the table given below,

Table 2

Class Frequency Class boundaries Midpoint
10.5011.49 92 10.49511.495 10.995
11.5012.49 78 11.49512.495 11.995
12.5013.49 68 12.49513.495 12.995
13.5014.49 45 13.49514.495 13.995
14.5015.49 34 14.49515.495 14.995

(d)

To determine

To find:

The relative frequency of each class for the given frequency distribution.

(d)

Expert Solution
Check Mark

Answer to Problem 8E

Solution:

The relative frequency of each class for the given frequency distribution is,

Class Frequency Class boundaries Midpoint Relative frequency
10.5011.49 92 10.49511.495 10.995 92317=29%
11.5012.49 78 11.49512.495 11.995 78317=25%
12.5013.49 68 12.49513.495 12.995 68317=21%
13.5014.49 45 13.49514.495 13.995 45317=14%
14.5015.49 34 14.49515.495 14.995 34317=11%

Explanation of Solution

Given:

The table is given as,

Hourly Wages of Surveillance
Operators (in Dollars)
Class Frequency
10.5011.49 92
11.5012.49 78
12.5013.49 68
13.5014.49 45
14.5015.49 34

Formula used:

The formula to calculate the relative frequency of any class is,

Relativefrequency=fN

Here N is the sum of the frequencies.

Calculation:

The sum of the frequencies is,

N=92+78+68+45+34=317

For the first class,

Substitute 92 for f and 317 for N in the formula,

Relative frequency=92317=0.29=29%

Continuing the same way, the relative frequency of all the five classes are shown in the table given below,

Table 3

Class Frequency Class boundaries Midpoint Relative frequency
10.5011.49 92 10.49511.495 10.995 92317=29%
11.5012.49 78 11.49512.495 11.995 78317=25%
12.5013.49 68 12.49513.495 12.995 68317=21%
13.5014.49 45 13.49514.495 13.995 45317=14%
14.5015.49 34 14.49515.495 14.995 34317=11%

(e)

To determine

To find:

The cumulative frequency of each class for the given frequency distribution.

(e)

Expert Solution
Check Mark

Answer to Problem 8E

Solution:

The cumulative frequency of each class for the given frequency distribution is,

Class Frequency Class boundaries Midpoint Relative frequency Cumulative frequency
10.5011.49 92 10.49511.495 10.995 92317=29% 92
11.5012.49 78 11.49512.495 11.995 78317=25% 92+78=170
12.5013.49 68 12.49513.495 12.995 68317=21% 170+68=238
13.5014.49 45 13.49514.495 13.995 45317=14% 238+45=283
14.5015.49 34 14.49515.495 14.995 34317=11% 283+34=317

Explanation of Solution

Given:

The table is given as,

Hourly Wages of Surveillance
Operators (in Dollars)
Class Frequency
10.5011.49 92
11.5012.49 78
12.5013.49 68
13.5014.49 45
14.5015.49 34

Formula used:

The cumulative frequency of any class is calculated by adding the frequency of that class and all the previous classes.

Calculation:

The cumulative frequency of all the five classes are shown in the table given below,

Table 4

Class Frequency Class boundaries Midpoint Relative frequency Cumulative frequency
10.5011.49 92 10.49511.495 10.995 92317=29% 92
11.5012.49 78 11.49512.495 11.995 78317=25% 92+78=170
12.5013.49 68 12.49513.495 12.995 68317=21% 170+68=238
13.5014.49 45 13.49514.495 13.995 45317=14% 238+45=283
14.5015.49 34 14.49515.495 14.995 34317=11% 283+34=317

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Beginning Statistics, 2nd Edition

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