30. Differentiate between retrospective cohort and case control studies (4 marks) 31. Describe numerical variables (3 marks) 32. Construct a grouped frequency table (5 marks) 33. Using the table you have constructed calculate and interpret the following: - a. Coefficient of variation (13 marks) b. The mode (5 marks) 60^th Percentile (5 marks) 34. Explain the term spectrum of disease. (2 marks)

30. **Differentiate between retrospective cohort and case control studies (4 marks)**<br /><br />- **Retrospective Cohort Study**: In a retrospective cohort study, the exposure status is determined at the start of the study, and the subjects are followed up to observe the occurrence of the outcome. This type of study looks back in time to examine exposures to suspected risk or protective factors in relation to an outcome.<br /><br />- **Case-Control Study**: In a case-control study, participants are selected based on whether they have the outcome of interest (cases) or not (controls). The exposure status is then determined retrospectively by asking participants about their past exposure. This type of study is useful for studying rare outcomes or diseases.<br /><br />31. **Describe numerical variables (3 marks)**<br /><br />Numerical variables, also known as quantitative variables, are variables that can take on numerical values and can be measured on a scale. They can be further classified into discrete and continuous variables.<br /><br />- **Discrete Variables**: These are variables that can take on a finite number of values. For example, the number of children in a family is a discrete variable because it can only take on whole number values (e.g., 0, 1, 2, etc.).<br /><br />- **Continuous Variables**: These are variables that can take on an infinite number of values within a given range. For example, height and weight are continuous variables because they can take on any value within a range (e.g., 5.5 feet, 70.2 kg, etc.).<br /><br />32. **Construct a grouped frequency table (5 marks)**<br /><br />To construct a grouped frequency table, follow these steps:<br /><br />1. Determine the range of the data by finding the minimum and maximum values.<br />2. Divide the range into intervals or classes.<br />3. Count the number of observations that fall within each interval.<br />4. Create a table with columns for the interval, lower limit, upper limit, and frequency.<br /><br />For example, if we have the following data: 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.<br /><br />| Interval | Lower Limit | Upper Limit | Frequency |<br />| --- | --- | --- | --- |<br />| 1-10 | 1 | 10 | 5 |<br />| 11-20 | 11 | 20 | 10 |<br />| 21-30 | 21 | 30 | 15 |<br />| 31-40 | 31 | 40 | 12 |<br />| 41-50 | 41 | 50 | 8 |<br />| 51-60 | 51 | 60 | 5 |<br />| 61-70 | 61 | 70 | 3 |<br />| 71-80 | 71 | 80 | 2 |<br />| 81-90 | 81 | 90 | 1 |<br />| 91-100 | 91 | 100 | 1 |<br /><br />33. **Using the table you have constructed calculate and interpret the following:**<br /><br />a. **Coefficient of Variation (13 marks)**<br /><br />The coefficient of variation (CV) is a measure of relative variability. It is calculated as the standard deviation divided by the mean, multiplied by 100. In this case, the CV would be calculated as follows:<br /><br />\[ CV = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 \]<br /><br />b. **The Mode (5 marks)**<br /><br />The mode is the value that appears most frequently in a data set. In this case, the mode would be the interval with the highest frequency, which is 21-30.<br /><br />c. **$60^{th}$ Percentile (5 marks)**<br /><br />The $60^{