Loose-leaf For Applied Statistics In Business And Economics
Loose-leaf For Applied Statistics In Business And Economics
5th Edition
ISBN: 9781259328527
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Textbook Question
Book Icon
Chapter 4.2, Problem 16SE

Spirit Airlines kept track of the number of empty seats on flight 308 (DEN-DTW) for 10 consecutive trips on each weekday except Friday. (a) Sort the data for each day. (b) Find the mean, median, mode, midrange, geometric mean, and 10 percent trimmed mean (i.e., dropping the first and last sorted observations) for each day. (c) Do the measures of center agree? Explain, (d) Note strengths or weaknesses of each statistic of center for the data.

Chapter 4.2, Problem 16SE, Spirit Airlines kept track of the number of empty seats on flight 308 (DEN-DTW) for 10 consecutive

a.

Expert Solution
Check Mark
To determine

Arrange the data.

Answer to Problem 16SE

The sorted data is:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 1

Explanation of Solution

Calculation:

The dataset represents the number of empty seats on flight 308 for 10 consecutive trips.

The data set of empty seats can be sorted either ascending or descending.

Here, the data is sorted in the ascending order.

Sorting:

Software procedure:

Step-by-step procedure to sort the data in ascending using the EXCEL is given below:

  • Open an EXCEL file.
  • Enter the data in the column  in H cells H1 to H10, column  in I cells I1 to I10, J cells J1 to J10 and column  in K cells K1 to K10.
  • Choose Data > Sort.
  • In Column drop down box, select Column H.
  • In Sort on drop down box, select Values.
  • In Order drop down box, select “Smallest to Largest”.
  • Click OK.
  •  In Column drop down box, select Column I.
  • In Sort on drop down box, select Values.
  • In Order drop down box, select “Smallest to Largest”.
  • Click OK.
  • In Column drop down box, select Column J.
  • In Sort on drop down box, select Values.
  • In Order drop down box, select “Smallest to Largest”.
  • Click OK.
  • In Column drop down box, select Column K.
  • In Sort on drop down box, select Values.
  • In Order drop down box, select “Smallest to Largest”.
  • Click OK.

Thus, the sorted data has been stored in the column in H cells H1 to H10, column  in I cells I1 to I10, J cells J1 to J10 and column  in K cells K1 to K10.

b.

Expert Solution
Check Mark
To determine

Find the Mean, Median, Mode, Midrange, Geometric mean, and 10% Trimmed mean.

Answer to Problem 16SE

The Mean, Median, Mode, Midrange, Geometric mean, and 10% Trimmed mean is:

Descriptive measuresMondayTuesdayWednesdayThursday
Mean44.703.801.90
Median5551
Mode1161
Geometric mean2.893.76Not applicable1.26
Midrange5555.50
Trimmed mean3.754.633.501

Explanation of Solution

Calculation:

For Monday:

Mean:

Software procedure:

Step-by-step software procedure to obtain Mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column I in cells I1 to I10.
  • In cell A1, enter the formula “=AVERAGE(I1:I10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 2

Thus, the mean number of empty seats on Monday is 4.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column I in cells I1 to I10.
  • In cell A1, enter the formula “=MEDIAN(I1:110)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 3

Thus, the median for the number of empty seats on Monday is 5.

Mode:

Software procedure:

Step-by-step software procedure to obtain Mode using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column I in cells I1 to I10.
  • In cell A1, enter the formula “=MODE.SNGL(I1:I10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 4

Thus, the mode for the number of empty seats on Monday is 1.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column I in cells I1 to I10.
  • In cell A1, enter the formula “=GEOMEAN(I1:I10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 5

Thus, the geometric mean for the number of empty seats on Monday is 2.89.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column I in cells I1 to I10.
  • In cell A1, enter the formula “=(MIN(I1:I10)+MAX(I1:I10))/2”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 6

  • Thus, the midrange for the number of empty seats on Monday is 5.

10% Trimmed mean:

Software procedure:

Step-by-step software procedure to obtain 10% Trimmed mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column I in cells I1 to I10.
  • In cell A1, enter the formula “=TRIMMEAN(I1:I10,0.2)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 7

  • Thus, the 10% Trimmed mean for the number of empty seats on Monday is 3.75.

For Tuesday:

Mean:

Software procedure:

Step-by-step software procedure to obtain Mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column J in cells J1 to J10.
  • In cell A1, enter the formula “=AVERAGE(J1:J10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 8

Thus, the mean number of empty seats on Tuesday is 4.70.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column J in cells J1 to J10.
  • In cell A1, enter the formula “=MEDIAN(J1:J10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 9

Thus, the median for the number of empty seats on Tuesday is 5.

Mode:

Software procedure:

Step-by-step software procedure to obtain Mode using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column J in cells J1 to J10.
  • In cell A1, enter the formula “=MODE.SNGL(J1:J10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 10

Thus, the mode for the number of empty seat on Tuesday is 1.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column J in cells J1 to J10.
  • In cell A1, enter the formula “=GEOMEAN(J1:J10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 11

Thus, the geometric mean for the number of empty seats on Tuesday is 3.76.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column J in cells J1 to J10.
  • In cell A1, enter the formula “=(MIN(J1:J10)+MAX(J1:J10))/2”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 12

  • Thus, the midrange for the number of empty seats on Tuesday is 5.

10% Trimmed mean:

Software procedure:

Step-by-step software procedure to obtain 10% Trimmed mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column J in cells J1 to J10.
  • In cell A1, enter the formula “=TRIMMEAN(J1:J10,0.2)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 13

  • Thus, the 10% Trimmed mean for the number of empty seats on Tuesday is 4.63.

For Wednesday:

Mean:

Software procedure:

Step-by-step software procedure to obtain Mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column K in cells K1 to K10.
  • In cell A1, enter the formula “=AVERAGE(K1:K10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 14

Thus, the mean number of empty seats on Wednesday is 3.80.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column K in cells K1 to K10.
  • In cell A1, enter the formula “=MEDIAN(K1:K10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 15

Thus, the median for the number of empty seats on Wednesday is 5.

Mode:

Software procedure:

Step-by-step software procedure to obtain Mode using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column K in cells K1 to K10.
  • In cell A1, enter the formula “=MODE.SNGL(K1:K10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 16

Thus, the mode for the number of empty seat on Wednesday is 6.

Geometric mean:

  • Here, the data set on Wednesday contains zero, so, geometric mean is not applicable.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column K in cells K1 to K10.
  • In cell A1, enter the formula “=(MIN(K1:K10)+MAX(K1:K10))/2”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 17

  • Thus, the midrange for the number of empty seats on Wednesday is 5.

10% Trimmed mean:

Software procedure:

Step-by-step software procedure to obtain 10% Trimmed mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column K in cells K1 to K10.
  • In cell A1, enter the formula “=TRIMMEAN(K1:K10,0.2)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 18

  • Thus, the 10% Trimmed mean for the number of empty seats on Wednesday is 3.50.

For Thursday:

Mean:

Software procedure:

Step-by-step software procedure to obtain Mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column L in cells L1 to L10.
  • In cell A1, enter the formula “=AVERAGE(L1:L10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 19

Thus, the mean number of empty seats on Thursday is 1.90.

Median:

Software procedure:

Step-by-step software procedure to obtain Median using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column L in cells L1 to L10.
  • In cell A1, enter the formula “=MEDIAN(L1:L10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 20

Thus, the median for the number of empty seats on Thursday is 5.

Mode:

Software procedure:

Step-by-step software procedure to obtain Mode using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column L in cells L1 to L10.
  • In cell A1, enter the formula “=MODE.SNGL(L1:L10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 21

Thus, the mode for the number of empty seat on Thursday is 1.

Geometric mean:

Software procedure:

Step-by-step software procedure to obtain Geometric mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column L in cells L1 to L10.
  • In cell A1, enter the formula “=GEOMEAN(L1:L10)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 22

Thus, the geometric mean for the number of empty seats on Thursday is 1.26.

Midrange:

Software procedure:

Step-by-step software procedure to obtain Midrange using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column L in cells L1 to L10.
  • In cell A1, enter the formula “=(MIN(L1:L10)+MAX(L1:L10))/2”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 23

  • Thus, the midrange for the number of empty seats on Thursday is 5.50.

10% Trimmed mean:

Software procedure:

Step-by-step software procedure to obtain 10% Trimmed mean using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data in the column L in cells L1 to L10.
  • In cell A1, enter the formula “=TRIMMEAN(L1:L10,0.2)”.
  • Output using EXCEL software is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 4.2, Problem 16SE , additional homework tip 24

  • Thus, the 10% Trimmed mean for the number of empty seats on Thursday is 1.

b.

Expert Solution
Check Mark
To determine

Explain whether or not the measures of center agreed.

Answer to Problem 16SE

No, the measures of center are not agreed.

Explanation of Solution

The measures of center will not acceptable for the number of empty seats on flight 308. In this situation, the mode and geometric mean are totally different from the other measures. That is, the mean, median and the midrange for all days in a week has the similar values.

c.

Expert Solution
Check Mark
To determine

Note the strength or weakness of the statistic of center.

Explanation of Solution

Strength of the statistic of the center:

Mean:  it is more preferable for any statistical analysis which uses all information about the sample data.

Median: median will be more unaffected by the extreme values.

Mode: Of all the observations, mode is the undependable measure of center.

Weakness of the statistic of the center:

Mean:  it is affected by the extreme values.

Median: it is affected by the gaps in the data value.

Mode: it is not helpful for continuous data.

When the strength or weakness is observed for each day, it is known that mode is the undependable for all the days. It is observed from the previous part (b), the mean and median are equal for all the days, so it acts as the strength of the statistic of center.

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Chapter 4 Solutions

Loose-leaf For Applied Statistics In Business And Economics

Ch. 4.2 - Prob. 1SECh. 4.2 - For each data set, is the mode a good measure of...Ch. 4.2 - For each data set, is the mode a good measure of...Ch. 4.2 - For each data set, which best indicates a typical...Ch. 4.2 - For each data set, which best indicates a typical...Ch. 4.2 - Days on the market are shown for the 36 most...Ch. 4.2 - Scores are shown for the most recent state civil...Ch. 4.2 - Prob. 8SECh. 4.2 - CitiBank recorded the number of customers to use a...Ch. 4.2 - Prob. 10SE
Ch. 4.2 - Prob. 11SECh. 4.2 - Prob. 12SECh. 4.2 - (a) Write the Excel function for the 10 percent...Ch. 4.2 - Prob. 14SECh. 4.2 - Prob. 15SECh. 4.2 - Spirit Airlines kept track of the number of empty...Ch. 4.2 - CitiBank recorded the number of customers to use a...Ch. 4.2 - On Friday night, the owner of Chez Pierre in...Ch. 4.2 - Prob. 19SECh. 4.2 - Prob. 20SECh. 4.3 - (a) Find the mean and standard deviation for each...Ch. 4.3 - For each data set: (a) Find the mean. (b) Find the...Ch. 4.3 - In fuel economy tests in city driving conditions,...Ch. 4.3 - Over the past month, Bobs bowling score mean was...Ch. 4.3 - Prob. 25SECh. 4.3 - Prob. 26SECh. 4.3 - (a) Find the coefficient of variation for prices...Ch. 4.3 - Prob. 28SECh. 4.3 - Noodles and Company tested consumer reaction to...Ch. 4.4 - (a) By Chebyshevs Theorem, at least how many...Ch. 4.4 - An exam has a mean of 70 with a standard deviation...Ch. 4.4 - Prob. 32SECh. 4.4 - The mean collection period for accounts receivable...Ch. 4.4 - Prob. 34SECh. 4.4 - Prob. 35SECh. 4.4 - Prob. 36SECh. 4.4 - Find the original data value corresponding to each...Ch. 4.4 - CitiBank recorded the number of customers to use a...Ch. 4.4 - Prob. 39SECh. 4.5 - Scores on an accounting exam ranged from 42 to 96,...Ch. 4.5 - In 2007, total compensation (in thousands of...Ch. 4.5 - Waiting times (minutes) for a table at Joeys BBQ...Ch. 4.5 - Coffee temperatures (degrees Fahrenheit) at a...Ch. 4.5 - Prob. 44SECh. 4.5 - On San Martin Boulevard, embedded sensors kept...Ch. 4.5 - Prob. 46SECh. 4.5 - Prob. 47SECh. 4.6 - For each X-Y data set (n = 12): (a) Make a scatter...Ch. 4.6 - Your laptop gets warm (even hot) when you place it...Ch. 4.6 - Prob. 50SECh. 4.6 - Prob. 51SECh. 4.7 - Estimate the mean from this table of grouped data...Ch. 4.7 - Estimate the mean from the following table of...Ch. 4 - What are descriptive statistics? How do they...Ch. 4 - Explain each concept: (a) center, (b) variability,...Ch. 4 - Prob. 3CRCh. 4 - List strengths and weaknesses of each measure of...Ch. 4 - Prob. 5CRCh. 4 - (a) What is a bimodal distribution? (b) Explain...Ch. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - (a) Which standard deviation formula (population,...Ch. 4 - (a) To what kind of data does Chebyshevs Theorem...Ch. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - (a) Explain the method of medians for calculating...Ch. 4 - (a) What is a box plot? What does it tell us? (b)...Ch. 4 - Prob. 17CRCh. 4 - Prob. 18CRCh. 4 - Prob. 19CRCh. 4 - (a) What is kurtosis? (b) Sketch a platykurtic...Ch. 4 - Prob. 54CECh. 4 - If the mean asset turnover for retail firms is...Ch. 4 - Prob. 56CECh. 4 - During a rock concert, the noise level (in...Ch. 4 - Bags of jelly beans have a mean weight of 396 gm...Ch. 4 - Based on experience, the Ball Corporations...Ch. 4 - SAT scores for the entering class of 2010 at...Ch. 4 - Prob. 61CECh. 4 - The average time a Boulder High varsity lacrosse...Ch. 4 - Prob. 63CECh. 4 - Below are monthly rents paid by 30 students who...Ch. 4 - How many days in advance do travelers purchase...Ch. 4 - The durations (minutes) of 26 electric power...Ch. 4 - The U.S. Postal Service will ship a Priority Mail...Ch. 4 - Prob. 68CECh. 4 - Prob. 69CECh. 4 - Prob. 70CECh. 4 - Prob. 71CECh. 4 - A plumbing suppliers mean monthly demand for vinyl...Ch. 4 - Prob. 73CECh. 4 - Prob. 74CECh. 4 - Prob. 75CECh. 4 - Caffeine content in a 5-ounce cup of brewed coffee...Ch. 4 - Prob. 77CECh. 4 - Prob. 78CECh. 4 - Prob. 79CECh. 4 - Prob. 80CECh. 4 - Prob. 81CECh. 4 - The median waiting time for a liver transplant in...Ch. 4 - A small suburban community agreed to purchase...Ch. 4 - A companys contractual trigger point for a union...Ch. 4 - Prob. 85CECh. 4 - (a) Enter the Excel function...Ch. 4 - Note: In each of the following tables, the upper...Ch. 4 - Prob. 88CECh. 4 - The self-reported number of hours worked per week...Ch. 4 - How long does it take to fly from Denver to...Ch. 4 - (a) Make an Excel scatter plot of X = 1990 assault...Ch. 4 - (a) Make an Excel scatter plot of X = airspeed...Ch. 4 - Prob. 95CECh. 4 - Prob. 1ERQCh. 4 - Which is not an ethical obligation of a...Ch. 4 - Prob. 3ERQCh. 4 - Prob. 4ERQCh. 4 - Give the type of measurement (nominal, ordinal,...Ch. 4 - Prob. 6ERQCh. 4 - To choose a sample of 12 students from a...Ch. 4 - Which of the following is not a reason for...Ch. 4 - Which statement is correct? Why not the others? a....Ch. 4 - Prob. 10ERQCh. 4 - The management of a theme park obtained a random...Ch. 4 - Which one of the following is true? Why not the...Ch. 4 - Prob. 13ERQCh. 4 - Prob. 14ERQCh. 4 - Here are the ages of a random sample of 20 CEOs...Ch. 4 - Prob. 16ERQCh. 4 - Prob. 17ERQCh. 4 - Prob. 18ERQCh. 4 - Which is not a characteristic of using a log scale...
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