Let's calculate the correlation between the total sales and each product category (Beverages, Snacks, and Meals) using Karl Pearson’s coefficient of correlation.

Data Extracted:

Formula for Karl Pearson’s Correlation:

[ r = \frac{N \sum XY - \sum X \sum Y}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 - (\sum Y)^2]}} ]

Where:

• $X$ = Total Sales
• $Y$ = Product Category (B, S, M)
• $N$ = Number of data points (5 in this case)

Let's perform the calculation step by step. numpy as np

Data

total_sales = np.array([100, 120, 140, 160, 180]) beverages = np.array([30, 35, 40, 45, 50]) snacks = np.array([40, 50, 60, 65, 70]) meals = np.array([30, 35, 40, 50, 60])

Pearson correlation calculation

corr_beverages = np.corrcoef(total_sales, beverages)[0, 1] corr_snacks = np.corrcoef(total_sales, snacks)[0, 1] corr_meals = np.corrcoef(total_sales, meals)[0, 1]

corr_beverages, corr_snacks, corr_meals### Correlation Results:

• Total Sales & Beverages: $r = 1.0$
• Total Sales & Snacks: $r \approx 0.985$
• Total Sales & Meals: $r \approx 0.985$

Interpretation:

• The correlation between total sales and beverages is perfect (1.0), indicating a linear relationship.
• The correlation between total sales and both snacks and meals is strong (0.985), suggesting a very high positive correlation.

Would you like to proceed with calculating Spearman’s rank correlation or have any other questions?

Here are 5 follow-up questions to consider:

1. What is the significance of a perfect correlation of 1?
2. How can you interpret the correlation between snacks and meals?
3. Can outliers affect the Pearson correlation coefficient?
4. How is Spearman's rank correlation different from Pearson’s?
5. What practical steps can the canteen take based on these results?

Tip: When interpreting correlation values, remember that correlation does not imply causation.