4. (i) Classify methods of statistical analysis and briefly explain the situations under which each may be employed. (ii) State the need of studying Statistics in your programme of study. What significant role does a statistician play in a scientific investigation? (iii) Distinguish between standard deviation and coefficient of variation. State two desirable properties of each of these measures of dispersion.

### (i) Classification of Methods of Statistical Analysis Statistical analysis can be broadly classified into two main categories: **Descriptive Statistics** and **Inferential Statistics**. 1. **Descriptive Statistics**: - **Definition**: This method involves summarizing and organizing data to describe its main features. - **Situations for Use**: - When you need to present data in a meaningful way, such as through graphs, charts, or summary statistics (mean, median, mode). - When analyzing a dataset to understand its basic characteristics without making predictions or generalizations. - Examples include calculating the average test score of a class or creating a histogram of age distribution in a population. 2. **Inferential Statistics**: - **Definition**: This method involves making predictions or inferences about a population based on a sample of data. - **Situations for Use**: - When you want to draw conclusions about a larger group from a smaller sample. - When conducting hypothesis testing to determine if there is enough evidence to support a specific claim. - Examples include estimating the average income of a population based on a survey of a sample or testing the effectiveness of a new drug based on clinical trial results. ### (ii) Need for Studying Statistics Studying statistics is essential in various fields for several reasons: 1. **Data Interpretation**: Statistics provides tools for analyzing and interpreting data, which is crucial for making informed decisions. 2. **Research and Development**: In scientific research, statistics helps in designing experiments, analyzing results, and validating findings. 3. **Quality Control**: In industries, statistical methods are used to monitor and improve quality in manufacturing processes. 4. **Policy Making**: Governments and organizations use statistical data to formulate policies and allocate resources effectively. **Role of a Statistician in Scientific Investigation**: - A statistician plays a critical role in designing experiments, ensuring that data collection methods are sound, and analyzing the data to draw valid conclusions. They help in: - Formulating hypotheses and determining the appropriate statistical tests. - Interpreting results and providing insights that guide decision-making. - Communicating findings clearly to stakeholders, ensuring that conclusions are based on solid statistical evidence. ### (iii) Distinction Between Standard Deviation and Coefficient of Variation 1. **Standard Deviation (SD)**: - **Definition**: A measure of the amount of variation or dispersion in a set of values. It quantifies how much the values deviate from the mean. - **Desirable Properties**: - **Sensitivity to Data Changes**: SD responds to changes in data, providing a clear indication of variability. - **Units of Measurement**: It is expressed in the same units as the data, making it easy to interpret in context. 2. **Coefficient of Variation (CV)**: - **Definition**: A standardized measure of dispersion calculated as the ratio of the standard deviation to the mean, often expressed as a percentage. It allows comparison of variability between datasets with different units or means. - **Desirable Properties**: - **Unitless Measure**: CV is dimensionless, allowing for comparison across different datasets regardless of their units. - **Relative Measure of Dispersion**: It provides insight into the relative variability of data, making it useful for comparing the degree of variation between different datasets. In summary, while both standard deviation and coefficient of variation measure dispersion, they serve different purposes and are used in different contexts based on the nature of the data and the analysis required.