Fundamentals of Data Science

Part 1: Understanding Data and Measurement (15 points)

Data and Information Hierarchy (5 points): Describe the difference between data, information, knowledge, and wisdom, explaining the hierarchical relationship among them. Provide a specific, real-world example to illustrate each level of the hierarchy.

Variables and Measurement Scales (10 points): Explain the different types of variables (nominal, ordinal, interval, and ratio), and describe the associated scales of measurement. Provide a specific example of each type of variable and explain why it is classified as such. 

Part 2: Descriptive Statistics and Bivariate Analysis (30 points) 

• Frequency Distribution and Summary Measures (15 points): Select a dataset (this could be publicly available data or a dataset from your workplace). Create a frequency distribution for a chosen variable, calculate common summary measures (mean, median, mode, range, variance, and standard deviation), and provide a short interpretation of these measures.
• Bivariate Analysis (15 points): With the same dataset or a different one, conduct a bivariate analysis that includes both an association between two qualitative variables and a correlation between two quantitative variables. Interpret your findings. 

Part 3: Probability and Distributions (30 points) 

Probability (10 points): Discuss the basic rules of probability, conditional probability, and Bayes’ theorem. Illustrate your discussion with unique examples.

Random Variables and Probability Distributions (20 points): Define discrete and continuous random variables. Give a real-world example of each and describe the associated probability distribution for each variable.

• Part 4: Sampling Techniques (20 points)
• Sampling (20 points): Define and differentiate random and non-random sampling. Discuss how to determine an appropriate sample size for a given study. Include an illustrative example from a real or hypothetical research study.