b. Outline six (6 ) properties of the mean (6marks) c. Calculate the 50^th percentile and interpret the answer (8 marks) 4. Describe the epidemiologic triad in relation to the principles of communicable disease control (20 marks)

b. Outline six (6) properties of the mean (6 marks):<br /><br />1. **Additivity**: The mean is additive, meaning that the mean of the sum of two variables is equal to the sum of their individual means.<br /><br />2. **Homogeneity of Variance**: The mean is not affected by changes in the scale of measurement. If all values in a dataset are multiplied by a constant, the mean will also be multiplied by the same constant.<br /><br />3. **Unbiasedness**: The mean is an unbiased estimator of the population mean. This means that the expected value of the sample mean is equal to the population mean.<br /><br />4. **Sensitivity to Outliers**: The mean is sensitive to outliers or extreme values. Adding a few very large or very small values to the dataset can significantly change the mean.<br /><br />5. **Non-negativity**: The mean is always non-negative for non-negative data. If all values in a dataset are non-negative, the mean will also be non-negative.<br /><br />6. **Symmetry**: The mean is symmetric about the center of the distribution. This means that the mean is the same whether you calculate it from the left side or the right side of the distribution.<br /><br />c. Calculate the $50^{th}$ percentile and interpret the answer (8 marks):<br /><br />To calculate the $50^{th}$ percentile, we need to find the value below which 50% of the data falls. This is also known as the median.<br /><br />To find the median, we first need to arrange the data in ascending order. If there is an odd number of data points, the median is the middle value. If there is an even number of data points, the median is the average of the two middle values.<br /><br />Once we have the median, we can interpret it as the value below which 50% of the data falls. This means that half of the data points are less than or equal to the median, and the other half are greater than or equal to the median.<br /><br />4. Describe the epidemiologic triad in relation to the principles of communicable disease control (20 marks):<br /><br />The epidemiologic triad consists of three components: the agent, the host, and the environment. The agent is the pathogen or disease-causing organism, such as a virus or bacteria. The host is the individual or population that is susceptible to the agent. The environment is the external factors that influence the transmission and spread of the agent.<br /><br />In relation to the principles of communicable disease control, the epidemiologic triad is important because it helps us understand the factors that contribute to the spread of infectious diseases. By targeting each component of the triad, we can implement effective control measures.<br /><br />For example, if we want to control the spread of a communicable disease, we can focus on reducing the agent by disinfecting surfaces or using personal protective equipment. We can also target the host by promoting hygiene practices and vaccination. Finally, we can modify the environment by implementing measures such as quarantine or isolation to prevent the spread of the agent.<br /><br />By understanding the epidemiologic triad and its components, we can develop targeted and effective strategies for controlling the spread of communicable diseases.