QUESTION ONE [35]
In a small town the distance of a sample of 122 randomly selected house from the entrance to the town’s main supermarket was measured to the nearest metre. The table below shows this information
| DISTANCE | FREQUENCY |
| [57; 60) | 9 |
| [60; 63) | 10 |
| [63; 66) | 18 |
| [66; 69) | 42 |
| [69; 72) | 27 |
| [72; 75) | 11 |
| [75; 78) | 5 |
Using appropriate computational formulas calculate:
- the average distance from the homes to the main supermarket (5)
- the median distance. (5)
- the modal distance. (5)
- the coefficient of variation for the above data (10)
- the mid-80% range the above data (5)
- Construct the ogive greater than ogive and show the median calculated in 1.2 above (5)
QUESTION TWO [25]
A lecturer at Regent Business School is convinced that he can predict the exam marks when given the assignment mark. He collected the assignment and exam marks of one of his undergraduate classes. The data is presented in the table below.
| ASSIGNMENT | EXAMINATION |
| 69 | 77 |
| 42 | 66 |
| 43 | 65 |
| 40 | 65 |
| 100 | 80 |
| 80 | 71 |
| 100 | 78 |
| 90 | 75 |
| 77 | 70 |
| 47 | 60 |
| 68 | 67 |
| 50 | 61 |
| 45 | 59 |
| 41 | 58 |
- Plot and comment on the possible relationship between the examination and the assignment marks (5)
- using appropriate computational formulae find the equation least-square regression line. (6)
- Interpret the y- intercepts of regression equation in question 2.2 above (4)
- Calculate the Pearson’s correlation coefficient for the above data (5)
- interpret the correlation coefficient calculate in question 2.4 above (5)
QUESTION THREE [20]
Shown in the table below are prices of 1 shot of scotch in a public bar, 1 kg of potatoes and 500 g of butter in Cape Town for September quarters in 1990 and 2020.
| Scotch(shot) | Potatoes(1kg) | Butter(500g) | ||
| 1990 | Units (million) sold | 36.9 | 42.0 | 22.5 |
| Unit price(R) | 8.1 | 4.1 | 10.9 | |
| 2020 | Units (million) sold | 43.5 | 60.8 | 27.6 |
| Unit price(R) | 31.6 | 10.9 | 18.9 |
Calculate and interpret
- Paasche’s price and quantity indices. (10)
- Laspereyes’ price and quantity indices. (10)
QUESTION FOUR [20]
A scientific trial into the efficacy a new COVID-19 vaccine was carried out. 120 Patients had comorbidity and 90 patients were in good health with no medical history. Out of those people, 50 females and 30 males had comorbidity. Given below is a contingency table with the given information filled in.
| Female | Male | Total | |
| Comorbidity | 50 | 30 | ? |
| Good health | ? | ? | ? |
| Total | 120 | 90 | ? |
4.1. Fill in the missing number in the above table (5) If a patient is chosen randomly what is the probability that:
- He/ She is in good health. (2)
- She is in good health and she is female? (2)
4.4. She is in good health given she is female (3)
4.5 Using calculation show whether or not health status is independent of gender? Explain. (8)
Answers to Statistics Assignment
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