Joint Frequency Distributions
2.1 EXERCISES
Excel 2016 Instructions 1. Place cursor in the Gender
numbers of the PivotTable.
2. Right click and select Value Field Settings.
3. On the Show values as tab, click on the down arrow and select % of Grand Total.
4. Click OK.
FIGURE 2.6 Excel 2016 Joint Relative Frequencies for Capital Credit Union
In Figure 2.6, we have used the Value Field Settings in the Excel PivotTable to represent the data as percentages.
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2-7. You are given the following data:
6 10 6 4 9 5
5 5 5 7 6 2
5 5 5 4 5 7
6 7 8 6 8 4
7 5 5 5 5 7
8 7 6 7 5 4
6 4 4 7 4 6
6 7 8 6 7 6
7 8 5 6 5 7
3 6 4 7 4 4
a. Construct a frequency distribution for these data.
b. Based on the frequency distribution, develop a histogram.
c. Construct a relative frequency distribution.
d. Develop a relative frequency histogram.
e. Compare the two histograms. Why do they look alike?
2-8. Using the data from Exercise 2-7:
a. Construct a grouped data relative frequency distribution of the data. Use the 2k Ú n guideline to determine the number of classes.
b. Construct a cumulative frequency distribution of the data.
c. Construct a relative frequency histogram.
d. Construct an ogive.
Business Applications
2-9. PLUSLine is a 24-hour PLUS toll free customer care line. The highway users can receive the latest traffic updates, lodge a feed, or request for PLUSRonda assistance on the PLUS expressways. The following are the average duration per call (in minutes) received in a day, for the previous two months, from motorists for roadside service:
26 14 18 9 21 23 17 10 24 17
7 11 15 17 13 16 22 14 23 18
25 8 21 5 12 15 19 20 21 11
27 16 12 19 20 25 24 6 15 23
14 18 13 27 23 14 17 29 14 13
23 17 18 10 9 4 19 13 6 17
12
a. Develop a frequency distribution for the average duration per call in a day. Discuss what the most concentration of the distribution tells you about the sample data.
b. Based on the results in part a, construct a frequency histogram for the sample data.
2-10. The owner of a toy shop conducts a survey of goods sold in the past two weeks. He sorts the toys into three categories—soft toys, educational toys, and physical activity toys with their respective sales per week. A total of 85 toys were sold in the past two weeks and showed an equal total sale of 30 for the soft toys and educational toys. The owner found that 60% of total sales were from the second week. At the same time, the educational toys in the first week and the physical activity toys in the second were sold with the same weightage of 20%.
a. Use the information to construct a joint frequency distribution.
b. Convert your part a distribution to a joint relative frequency distribution and round up your answers to two decimal places.
c. Determine the best-selling toy for each week.
d. What percentage of the total toy sales do the educational toys and physical activity toys sold in second week constitute?
2-11. A developer is launching their new developments for two types of housing. During the launching, the sales representatives will show and explain the show units for both types of housing to the customers. To provide better services, the management asked the sales representatives to record their customers’ satisfactions on their preferable type of housing by using the following codes and scales:
Housing Code Satisfaction A = Apartment 1 = Low B = Tower block 2 = Medium
3 = High The following are the sample record provided by their
customers:
Housing
Code Satisfaction Housing
Code Satisfaction
B 3 B 2
B 2 A 3
A 1 A 2
B 2 B 3
A 3 B 1
A 3 B 1
A 2 A 3
B 1 A 2
B 3 B 3
B 2 B 2
2.1 Frequency Distributions and Histograms
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Chapter 2 71M02_GROE0383_10_GE_C02.indd 71 05/09/17 2:08 PM
72 Chapter 2
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Graphs, Charts, and Tables—Describing Your Dataa. Construct two separate distributions for each of the variables with their respective frequency and relative frequency.
b. Construct a joint frequency distribution for these two variables.
c. Construct a joint relative frequency distribution for these two variables and write a short report for the distribution.
2-12. A St. Louis–based shipping company recently selected a random sample of 49 airplane weight slips for crates shipped from an automobile parts supplier. The weights, measured in pounds, for the sampled crates are as follows:
89 83 97 101 86 89 86
91 84 89 87 93 86 90
86 92 92 88 88 92 86
93 80 93 77 98 94 95
94 88 95 87 99 98 90
91 87 89 89 96 88 94
95 79 94 86 92 94 85
a. Create a data array of the weights.
b. Develop a frequency distribution using five classes having equal widths.
c. Develop a histogram from the frequency distribution you created in part b.
d. Develop a relative frequency and a cumulative relative frequency distribution for the weights using the same five classes created in part b. What percent of the sampled crates have weights greater than 96 pounds?
2-13. Aria is an assistant HR manager. She is helping the manager shortlist candidates by their required salary for the post of management trainee. The following are the required salary (in $) from 50 candidates:
3,000 2,500 3,250 2,950 2,900 4,000 3,100 2,700 2,850 2,600 3,700 3,250 2,750 2,480 2,300 3,640 3,680 3,360 3,250 2,950 2,800 2,780 3,110 2,670 3,450 2,650 3,750 3,150 2,780 3,580 4,000 3,600 3,650 4,200 3,560 2,700 2,900 3,250 2,650 3,200 2,500 3,150 2,630 2,145 2,770 3,250 2,580 2,580 3,850 3,350
a. Determine the appropriate number of classes for the required salary.
b. Use finding in part a, and find the class width for the required salary.
c. Construct a cumulative relative frequency distribution for the required salary.
d. Construct an ogive for the required salary. If the manager plans to interview the bottom 70% of the interviewees based on the required salary, what is the maximum required salary she will consider for the interview?
2-14. A café recently conducted a survey on its coffee selling by customers’ age. The owner recorded the first 30 customers who visited his café and had chosen coffee as their drink. The customers’ respective ages were recorded in a sample data set as follows:
23 45 28 37 48 51 18 23 13 52
41 21 29 19 20 36 44 37 27 52
37 36 26 27 17 45 39 33 22 36
a. Sort the customers’ age from the youngest to the oldest.
b. Construct a frequency distribution with five equal widths classes.
c. Use the frequency distribution in part b to develop a histogram.
d. Add two more columns which show the relative frequency and cumulative frequency for the frequency distribution in part b. Determine how many percent of the café’s customers chosen to drink coffee are less than 29 years old.
2-15. One effect of the great recession was to lower the interest rate on fixed-rate mortgages. A sample of 30-year fixed-rate mortgage rates taken from financial institutions in the Pacific Northwest resulted in the following:
3.79 4.03 3.92 3.87 3.86
3.93 3.87 3.69 3.99 3.88
3.91 3.81 3.85 3.81 3.65
4.15 3.98 3.82 4.08 3.84
3.95 4.03 3.96 3.69 3.97
4.08 3.86 3.82 3.83 4.19
3.49 3.49 3.75 3.46 3.92
3.67 3.63 3.81 3.86 4.15
3.85 4.01 3.93 4.02 4.09
a. Using Excel, construct a histogram with eight classes.
b. Determine the proportion of 30-year fixed mortgage rates that are at least 3.76%.
c. Produce an ogive for the data.
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2.1 Frequency Distributions and Histograms