Case Study: Using Statistics to Drive Business Decisions

The Problem Statement

Our retail company wants to understand its sales performance and marketing effectiveness to make better business decisions. We have 3 years of sales data containing:

• Monthly revenue
• Store types (online vs physical)
• Geographic regions
• Marketing spending
• Units sold
• Campaign participation

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Statistical Methods Used & Key Findings

1. Descriptive Statistics - Understanding Our Sales

Methods Applied:

• Central Tendency: Mean, median, mode
• Dispersion: Range, variance, standard deviation
• Distribution Shape: Histogram analysis

Key Findings:

• **Median revenue = 7723.325 (better representation than mean due to outliers)
• **Standard deviation = 4279.96146861139 (high variability → unstable sales month-to-month)
• Positively skewed distribution - Most months have moderate revenue, but some exceptional months pull the average up

Business Implication: Use median for sales planning, not average. High variability suggests we need to understand what causes sales spikes.

2. Data Visualization - Seeing Patterns

Visualizations Created:

1. Line chart: Revenue shows seasonal patterns
2. Bar chart: Online stores generate less revenue than physical stores
3. Box plot: Central region has highest median revenue
4. Scatter plot: Strong correlation between units sold and revenue

Business Implication:

• Invest more in physical infrastructure
• Investigate what drives Rift valley region's occasional exceptional performance
• Focus marketing on increasing units sold (directly impacts revenue)

3. Sampling Concepts - Avoiding Bad Decisions

Key Insights:

• Our full dataset (3 years) is the population
• If we only analyzed urban stores, we'd have undercoverage bias
• Better approach: Stratified random sampling by region type

Business Implication: Never make decisions based on biased samples. Ensure all customer/store types are represented in analysis.

4. Error Awareness - Cost of Mistakes

Type I Error Example (False Positive):

• Saying there's an effect/difference when there actually isn't

Type II Error Example (False Negative):

• Saying there's no effect when there actually is one

Business Implication: Balance risk. For expensive changes, require stronger evidence . For potential opportunities, avoid missing them (ensure adequate statistical power).

Business Recommendations

1. Revenue Planning: Use median not mean for budgeting due to outliers
2. Channel Strategy: Increase investment in physicsl stores
3. Marketing: Continue the successful campaign to more stores
4. Data Collection: Implement stratified sampling for future studies
5. Regional Focus: Investigate Northeast region's best practices

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This case study shows how statistical thinking transforms from abstract numbers to concrete business actions that can increase revenue, reduce risk, and optimize resource allocation.