a) Tabular representation/summary of Number of years in operation:
The tabular representation of the random variable Number of years in operation can be a frequency table that lists the number of businesses or organizations that fall into different categories of years in operation. For example:
Number of Years in Operation Number of Businesses/Organizations
0-5 200
6-10 150
11-15 100
16-20 50
Over 20 25
Interpretation: This table shows the distribution of businesses or organizations by their number of years in operation. The majority of businesses have been in operation for 0-5 years, followed by 6-10 years. A smaller number of businesses have been in operation for 11-15 years, 16-20 years, or over 20 years.
b) Cross-tabulation of Daily Income and Type of service:
The cross-tabulation of Daily Income and Type of service can be a table that shows the number of businesses or organizations that fall into different categories of both variables. For example:
Type of Service Daily Income Number of Businesses/Organizations
A 0-500 50
A 501-1000 75
A 1001-1500 25
A 1501-2000 10
B 0-500 20
B 501-1000 50
B 1001-1500 70
B 1501-2000 30
C 0-500 10
C 501-1000 20
C 1001-1500 30
C 1501-2000 40
Interpretation: This table shows the distribution of businesses or organizations by both their daily income and type of service.
For example, we can see that among businesses that provide service type A, the majority (75) fall into the 501-1000 daily income category, while among businesses that provide service type B, the majority (70) fall into the 1001-1500 daily income category.
c) Relative measures of variability for Daily Income by Type of service:
To calculate and interpret relative measures of variability for Daily Income by Type of service, we can use measures such as the coefficient of variation (CV) or the interquartile range (IQR). For example, we can calculate the CV and IQR for each of the three types of service separately and compare them. A lower CV or IQR indicates lower variability or dispersion of the data.
Interpretation: For example, if the CV of daily income for type A is lower than the CV of daily income for type B and C, this indicates that businesses that provide type A service have lower variability in their daily income than those that provide type B or C service. Similarly, if the IQR of daily income for type B is higher than the IQR of daily income for type A and C, this indicates that businesses that provide type B service have higher variability in their daily income