Loose Leaf for Statistical Techniques in Business and Economics
Loose Leaf for Statistical Techniques in Business and Economics
17th Edition
ISBN: 9781260152647
Author: Douglas A. Lind
Publisher: McGraw-Hill Education
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Chapter 2, Problem 52DA

a.

To determine

Obtain a frequency distribution for the variable Team salary.

Find the typical salary for a team.

Find the range of the salaries.

a.

Expert Solution
Check Mark

Answer to Problem 52DA

The frequency distribution for the salary is given below:

Salary $1,000,000’sNumber of teamsCumulative frequency
60-1001010
100-1401222
140-180628
180-220129
220-260130
Total30 

The typical salary of a team is from 100 to 400 million dollars.

The range of the salaries is 200 million dollars.

Explanation of Solution

Selection of number of classes:

“2 to the k rule” suggests that the number of classes is the smallest value of k, where 2k is greater than the number of observations.

It is given that the data set consists of 30 observations. The value of k can be obtained as follows:

24=16<3025=32>30

Here, k=5 is the smallest value for which 2k is greater than the number of observations.

Therefore, the number of classes for the given data set is 5.

From the data set Team salary, the maximum and minimum values are 230.4 and 65.8, respectively.

The formula for the class interval is given as follows:

i(Maximum valueMinimum value)k

Where, i is the class interval and k is the number of classes.

Therefore, the class interval for the given data can be obtained as follows:

i(Maximum valueMinimum value)k230.465.8532.92

In practice, the class interval size is usually rounded up to some convenient number. Therefore, the reasonable class interval is 40.

Frequency distribution:

The frequency table is a collection of mutually exclusive and exhaustive classes, which shows the number of observations in each class.

Since the minimum value is 65.8 and the class interval is 40, the first class would be 60–100. The frequency distribution for salary can be constructed as follows:

Salary $1,000,000’sNumber of teamsCumulative frequency
60-1001010
100-1401210+12=22
140-180622+6=28
180-220128+1=29
220-260129+1=30
Total30 

From the above frequency distribution, the typical salary of a team is from 100 to 400 million dollars.

The range of the salaries is from 60 to 260 million dollars. Thus, range of the salaries is 200 million dollars.

b.

To determine

Make a comment on shape of the distribution.

Check whether there are any teams that have a salary out of the line with the others.

b.

Expert Solution
Check Mark

Answer to Problem 52DA

The distribution of salaries is positively skewed.

There are two teams with salaries much higher than the remaining 28 team salaries.

Explanation of Solution

From the frequency distribution in Part (a), 22 out of 30 teams fall in first and second classes. Therefore, the distribution of salaries is positively skewed.

There are two teams with salaries much higher than the remaining 28 team salaries. These two teams have a salary out of the line with the others.

c.

To determine

Create a cumulative relative frequency polygon for the frequency distribution.

Identify the amount that is less than for the 40% of the team’s salary.

Find the number of teams that have a total salary of more than $220 million.

c.

Expert Solution
Check Mark

Answer to Problem 52DA

The cumulative frequency polygon for the given data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 2, Problem 52DA

There are 40% of the teams that have salary less than 90 million dollars.

There is only one team that is getting salary more than 220 million dollars.

Explanation of Solution

For the given data set, the cumulative relative frequency table with midpoints of classes is obtained as follows:

Salary$1,000,000’sMidpointCumulative frequencyRelative cumulative frequency
60-10060+1002=80101030=0.33
100-140100+1402=120222230=0.73
140-180140+1802=160282830=0.93
180-220180+2202=200292930=0.97
220-260220+2602=240303030=1.00

The cumulative relative frequency polygon for the given data can be drawn using EXCEL.

Step-by-step procedure to obtain the frequency polygon using EXCEL is as follows:

  • Enter the column of midpoints along with the cumulative relative frequency column.
  • Select the total data range with labels.
  • Go to Insert > Charts > line chart.
  • Select the appropriate line chart.
  • Click OK.

From the above cumulative relative frequency polygon, 40% of the teams have salary less than 90 million dollars.

There are 3% of the teams that get salary more than 220 million dollars. In the given data, 3% of teams are equal to 1 team. Thus, only one team is getting salary more than 220 million dollars.

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Chapter 2 Solutions

Loose Leaf for Statistical Techniques in Business and Economics

Ch. 2 - A set of data consists of 45 observations between...Ch. 2 - A set of data consists of 230 observations between...Ch. 2 - A set of data contains 53 observations. The...Ch. 2 - Wachesaw Manufacturing Inc. produced the following...Ch. 2 - The Quick Change Oil Company has a number of...Ch. 2 - The manager of the BiLo Supermarket in Mt....Ch. 2 - The food services division of Cedar River...Ch. 2 - The annual imports of a selected group of...Ch. 2 - Mollys Candle Shop has several retail stores in...Ch. 2 - The following chart shows the number of patients...Ch. 2 - The following frequency distribution reports the...Ch. 2 - Prob. 18ECh. 2 - A sample of the hourly wages of 15 employees at...Ch. 2 - The following cumulative frequency and the...Ch. 2 - The cumulative frequency and the cumulative...Ch. 2 - The frequency distribution representing the number...Ch. 2 - Prob. 22ECh. 2 - Describe the similarities and differences of...Ch. 2 - Describe the similarities and differences between...Ch. 2 - Alexandra Damonte will be building a new resort in...Ch. 2 - Prob. 26CECh. 2 - A data set consists of 83 observations. How many...Ch. 2 - A data set consists of 145 observations that range...Ch. 2 - The following is the number of minutes to commute...Ch. 2 - The following data give the weekly amounts spent...Ch. 2 - A social scientist is studying the use of iPods by...Ch. 2 - David Wise handles his own investment portfolio,...Ch. 2 - You are exploring the music in your iTunes...Ch. 2 - The monthly issues of the Journal of Finance are...Ch. 2 - The following histogram shows the scores on the...Ch. 2 - The following chart summarizes the selling price...Ch. 2 - A chain of sport shops catering to beginning...Ch. 2 - The numbers of outstanding shares for 24 publicly...Ch. 2 - A recent survey showed that the typical American...Ch. 2 - Midland National Bank selected a sample of 40...Ch. 2 - Residents of the state of South Carolina earned a...Ch. 2 - A recent study of home technologies reported the...Ch. 2 - Merrill Lynch recently completed a study regarding...Ch. 2 - A total of 5.9% of the prime-time viewing audience...Ch. 2 - Refer to the following chart: a. What is the name...Ch. 2 - The following chart depicts the annual revenues,...Ch. 2 - Prob. 47CECh. 2 - Prob. 48CECh. 2 - One of the most popular candies in the United...Ch. 2 - The number of families who used the Minneapolis...Ch. 2 - Refer to the North Valley Real Estate data that...Ch. 2 - Prob. 52DACh. 2 - Refer to the Lincolnville School District bus...
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