Applied Statistics in Business and Economics
5th Edition
ISBN: 9781259329050
Author: DOANE
Publisher: MCG
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Chapter 4, Problem 85CE
a.
To determine
Find the
a.
Expert Solution
Answer to Problem 85CE
The Mean and Standard deviation is:
| Measures | Week 1 | Week 2 | Week 3 | Week 4 |
| Mean | 50 | 50 | 50 | 50 |
| Standard deviation | 10.61 | 10.61 | 10.61 | 10.61 |
Explanation of Solution
Calculation:
The data represents the weekend occupancy rates in the nine resort hotels at the time of off season.
For Week 1:
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 I9.
- In cell A1, enter the formula “=AVERAGE(I1:I9)”.
- Output using EXCEL software is given below:
Thus, the mean for Week 1 is 50.
Standard deviation:
Software procedure:
Step-by-step software procedure to obtain Standard deviation using EXCEL software is as follows:
- Open an EXCEL file.
- Enter the data in the column I in cells I1 to I9.
- In cell A1, enter the formula “=STDEV(I1:19)”.
- Output using EXCEL software is given below:
Thus, the Standard deviation for Week 1 is 10.61.
For Week 2:
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 J9.
- In cell A1, enter the formula “=AVERAGE(J1:J9)”.
- Output using EXCEL software is given below:
Thus, the mean for the week 2 is 50.
Standard deviation:
Software procedure:
Step-by-step software procedure to obtain Standard deviation using EXCEL software is as follows:
- Open an EXCEL file.
- Enter the data in the column J in cells J1 to J9.
- In cell A1, enter the formula “=STDEV(J1:J9)”.
- Output using EXCEL software is given below:
Thus, the Standard deviation for Week 2 is 10.61.
For Week 3:
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 K9.
- In cell A1, enter the formula “=AVERAGE(K1:K9)”.
- Output using EXCEL software is given below:
Thus, the mean for Week 3 is 50.
Standard deviation:
Software procedure:
Step-by-step software procedure to obtain Standard deviation using EXCEL software is as follows:
- Open an EXCEL file.
- Enter the data in the column K in cells K1 to K9.
- In cell A1, enter the formula “=STDEV(K1:K9)”.
- Output using EXCEL software is given below:
Thus, the Standard deviation for Week 3 is 10.61.
For Week 4:
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 L9.
- In cell A1, enter the formula “=AVERAGE(L1:L9)”.
- Output using EXCEL software is given below:
Thus, the mean for Week 4 is 50.
Standard deviation:
Software procedure:
Step-by-step software procedure to obtain standard deviation using EXCEL software is as follows:
- Open an EXCEL file.
- Enter the data in the column L in cells L1 to L9.
- In cell A1, enter the formula “=STDEV(L1:L9)”.
- Output using EXCEL software is given below:
Thus, the Standard deviation for Week 4 is 10.61.
b.
To determine
Write the conclusion based on the measures of center and variability.
b.
Expert Solution
Explanation of Solution
By observing the values of mean and standard deviation, it states that the occupancy rate in the hotels is same for all the week ends during offseason. Therefore, it can be concluded that the distribution of the occupancy rate is normal.
c.
To determine
Calculate the
c.
Expert Solution
Answer to Problem 85CE
The Median for the occupancy rates is:
| Measures | Week 1 | Week 2 | Week 3 | Week 4 |
| Median | 50 | 52 | 56 | 47 |
Explanation of Solution
For Week 1:
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 I9.
- In cell A1, enter the formula “=MEDIAN(I1:19)”.
- Output using EXCEL software is given below:
Thus, the median for Week 1 is 50.
For Week 2:
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 J9.
- In cell A1, enter the formula “=MEDIAN(J1:J9)”.
- Output using EXCEL software is given below:
Thus, the median for Week 2 is 52.
For Week 3:
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 K9.
- In cell A1, enter the formula “=MEDIAN(K1:K9)”.
- Output using EXCEL software is given below:
Thus, the median for Week 3 is 56.
For Week 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 L in cells L1 to L9.
- In cell A1, enter the formula “=MEDIAN(L1:L9)”.
- Output using EXCEL software is given below:
Thus, the median for Week 4 is 47.
d.
To determine
Construct dot plot for each sample.
d.
Expert Solution
Answer to Problem 85CE
The dot plot for Week 1 is as follows:
The dot plot for Week 2 is as follows:
The dot plot for Week 3 is as follows:
The dot plot for Week 4 is as follows:
Explanation of Solution
Dot plot:
Procedure to draw a dot plot for Week 1:
- Draw a horizontal line and mark the points from 30 to 70 with 5-point scale
- For week 1, mark a point corresponding to each observation along the horizontal line.
Procedure to draw a dot plot for Week 2:
- Draw a horizontal line and mark the points from 30 to 70 with 5-point scale
- For week 2, mark a point corresponding to each observation along the horizontal line.
Procedure to draw a dot plot for Week 3:
- Draw a horizontal line and mark the points from 36 to 64 with 4-point scale
- For week 3, mark a point corresponding to each observation along the horizontal line.
Procedure to draw a dot plot for Week 4:
- Draw a horizontal line and mark the points from 35 to 70 with 5-point scale
- For week 4, mark a point corresponding to each observation along the horizontal line.
Thus, the dot plot has been obtained for Week 1, Week 2, Week 3 and Week 4.
e.
To determine
Describe the things that have been learnt from the median and dot plot, that was not apparent from the means and standard deviation.
e.
Expert Solution
Explanation of Solution
The distribution of the occupancy rate is normal based on the value of mean and standard deviation. However, the median value and dot plot states that the distribution of the occupancy rate is little bit different.
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28212
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Number of Hours Frequency Relative Frequency
10-19
20-29
|30-39
40-49
50-59
60-69
70-79
80-89
From the frequency table above, find
a) the lower class limits
b) the upper class limits
c) the class width
d) the class boundaries
Statistics 300
Frequency Tables and Pictures of Data, page 2
Using your frequency table, construct a frequency and a relative frequency
histogram labeling both axes.
Table of hours of television watched per week:
11
15 24
34
36
22
20
30
12
32
24
36
42
36
42
26
37
39
48
35
26
29
27
81276
40
54
47
KARKE
31
35
42
75
35
46
36
42
65
28
54 65
28
23
28
23669
34
43 35 36
16
19
19
28212
Using the data above, construct a frequency table according the following
classes:
Number of Hours Frequency Relative Frequency
10-19
20-29
|30-39
40-49
50-59
60-69
70-79
80-89
From the frequency table above, find
a) the lower class limits
b) the upper class limits
c) the class width
d) the class boundaries
Statistics 300
Frequency Tables and Pictures of Data, page 2
Using your frequency table, construct a frequency and a relative frequency
histogram labeling both axes.
Chapter 4 Solutions
Applied Statistics in Business and Economics
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