APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Textbook Question
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
a.
Expert Solution
To determine
Arrange the data.
Answer to Problem 16SE
The sorted data is:
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
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 measures | Monday | Tuesday | Wednesday | Thursday |
| Mean | 4 | 4.70 | 3.80 | 1.90 |
| Median | 5 | 5 | 5 | 1 |
| Mode | 1 | 1 | 6 | 1 |
| Geometric mean | 2.89 | 3.76 | Not applicable | 1.26 |
| Midrange | 5 | 5 | 5 | 5.50 |
| Trimmed mean | 3.75 | 4.63 | 3.50 | 1 |
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:
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:
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:
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:
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:
- 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:
- 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:
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:
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:
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:
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:
- 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:
- 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:
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:
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:
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:
- 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:
- 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:
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:
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:
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:
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:
- 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:
- Thus, the 10% Trimmed mean for the number of empty seats on Thursday is 1.
b.
Expert Solution
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
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
APPLIED STAT.IN BUS.+ECONOMICS
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- For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of months unemployed and the values in the second column show the corresponding number of unemployed persons. Months Unemployed Number Unemployed 1 1029 2 1686 3 2269 4 2675 5 3487 6 4652 7 4145 8 3587 9 2325 10 1120 Let x be a random variable indicating the number of months a person is unemployed. a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals). (x) f(x) 1 2 3 4 5 6 7 8 9 10 b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution. The input in the box below will not be graded, but may be reviewed and considered by your instructor. c. What is the probability that a person…arrow_forwardIn Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 4 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardIn Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 2 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forward
- A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Duration of Call x f(x) 1 2 3 4 Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forwardA psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. x f(x) for x = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(x) ≥0 Σf(x) = 1 (5.1) (5.2) Does this probability distribution satisfy equation (5.1)? Select Does this probability distribution satisfy equation (5.2)? Select b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forward
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