Covid-19 took the world by storm and by April 2020, large numbers of people around the world were tested positive for the virus.
In the frequency distribution below, the number of people infected in 40 different countries are given.
| Hundreds of thousands of people infected | Number of countries |
| [1.0 ; 3.0) | 5 |
| [3.0 ; 5.0) | 8 |
| [5.0; 7.0) | 17 |
| [7.0 ; 9.0) | 6 |
| [9.0; 11.0) | 3 |
| [11.0; 13.0) | 1 |
| TOTAL | 40 |
- Calculate the estimated mean number of people infected in these 40 countries.
- Compute the median.
- Calculate the mode.
- What information about the skewness of the data can be inferred from your answers to (1.1), (1.2) and (1.3) above?
- Calculate the coefficient of variation for the above data
- Calculate the mid-50% range the above data
- Construct the ogive greater than ogive and show the median calculated in 1.2 above
An insurance manager believes that the number of new policies written annually by his agents is related to the number of years of selling experience that these agents have.
A random sample of 12 agents revealed the data in the table below:
| Number of years of experience | Number of new policies written annually |
| 2 | 17 |
| 5 | 22 |
| 7 | 34 |
| 6 | 37 |
| 12 | 50 |
| 9 | 41 |
| 5 | 13 |
| 20 | 48 |
| 13 | 39 |
| 4 | 20 |
| 10 | 35 |
| 20 | 63 |
For the above data:
- determine the dependent and the independent variable
- using appropriate computational formulae find the least-square regression line.
- Interpret the y- intercepts of regression equation in question 2.2 above
- Calculate the Pearson’s correlation coefficient for the above data
- interpret the correlation coefficient calculate in question 2.4 above
- Predict the number of policies written annually by an agent with 3 years of experience.
Question Three: Data in the table below show the prices and quantities of 3 products. (Use 2020 as the base year)
| Product | 2020 | 2021 | ||
| Price | Quantity | Price | Quantity | |
| I | 5 | 25 | 7 | 52 |
| II | 10 | 40 | 15 | 70 |
| III | 7 | 30 | 10 | 100 |
Calculate and interpret
- Paasche’s price and quantity indices and interpret you finding.
- Laspereyes’ price and quantity indices
Question 4: The data in the table below pertains to employees of a large oil refining firm in Durban.
| Age | Diploma | BCom | MBA |
| Under 30 | 32 | 20 | 12 |
| Between 30 and 40 | 48 | 40 | 13 |
| Over 40 | 20 | 10 | 5 |
If an employee is selected at random from this population, calculate the probability that the employee:
- is over 40
- holds an MBA
- holds a diploma and between 30-40 years of age.
- is under 30, given that he/she has a diploma.
- holds a BCom degree or is over 40 years.
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