Chapter 4, Problem 87CE

a.

To determine

Find the Mean and Standard deviation.

Answer to Problem 87CE

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.

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 median for the each week.

Answer to Problem 87CE

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.

Answer to Problem 87CE

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.

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.