Module 2 — Statistical Foundations for Business

Statistics for business begins with understanding how to summarise data. Measures of central tendency — mean, median, and mode — each tell a different story about the "centre" of your data.

The mean (average) is useful but sensitive to outliers. A company's average salary might be skewed by a highly paid CEO. The median (middle value) is more robust and better represents the typical case when data is skewed. The mode (most frequent value) is useful for categorical data — the most popular product, the most common complaint type.

Measures of dispersion describe how spread out data is. The range (max - min) gives a quick sense but is distorted by outliers. Standard deviation measures how far values typically fall from the mean — a low standard deviation means data clusters tightly around the average, while a high standard deviation indicates wide variation.

In business contexts, understanding variability is often more important than knowing the average. Two sales teams with the same average revenue but different variability have very different risk profiles. A customer satisfaction score of 4.0 could mean "everyone rates us 4" or "half rate us 5 and half rate us 3" — very different strategic implications.

Hypothesis testing provides a rigorous framework for making decisions based on data. The process:

1. State a null hypothesis (H₀): "There is no difference/effect" (the status quo) 2. State an alternative hypothesis (H₁): "There is a difference/effect" (what you're testing) 3. Collect data and calculate a test statistic 4. Determine the p-value: the probability of observing your results if H₀ is true 5. Decision: If p-value < significance level (typically 0.05), reject H₀

In business, hypothesis testing powers A/B testing: comparing two versions of a webpage, email, or product feature to determine which performs better. The key is ensuring the sample size is large enough and running the test long enough to detect a meaningful difference.

Correlation vs. causation is perhaps the most important concept in applied statistics. A correlation between two variables means they tend to move together — but this does NOT mean one causes the other. Ice cream sales and drowning deaths are correlated (both increase in summer), but ice cream doesn't cause drowning. Temperature is the confounding variable.

Establishing causation requires controlled experiments (like A/B tests) where you manipulate one variable while holding others constant. When experiments aren't possible, statistical techniques like regression analysis can help identify relationships, but interpreting them as causal requires careful reasoning about mechanisms and alternative explanations.