Maya always ships her packages using one of two shipping companies. At Company 1, Maya pays €3.00 per kilogram based...

Phase 1: Owning the Dataset

Visualization Selection

Since we're comparing two companies with different pricing structures, we'll use a comparison table:

Key Information

• Maya shipped 27 packages using Company 1 last year
• Average weight of those packages: \(2.50 \text{ kg}\)
• She always chooses the cheaper option

Phase 2: Understanding the Question

We need to find two values:

1. Average price: The average price Maya paid per package using Company 1
2. Average amount saved: How much she saved on average by choosing Company 1 over Company 2

Key Insight

Since Maya chose Company 1 for these packages, it must have been cheaper than Company 2's \(€14.00\) flat fee for each of them.

Phase 3: Finding the Answer

Calculating Average Price (Company 1)

• Price formula for Company 1: \(\mathrm{Price} = \mathrm{Weight} \times €3.00/\mathrm{kg}\)
• Average weight = \(2.50 \text{ kg}\)
• Average price = \(2.50 \text{ kg} \times €3.00/\mathrm{kg} = €7.50\)

Calculating Average Savings

• Company 2 would have charged: \(€14.00\) per package (flat fee)
• Company 1 average charge: \(€7.50\) per package
• Average savings = \(€14.00 - €7.50 = €6.50\)

Verification

This makes sense because Maya chose Company 1, meaning it was cheaper. At \(2.50 \text{ kg}\) average weight, Company 1 charges \(€7.50\), which is indeed less than Company 2's \(€14.00\).

Phase 4: Solution

Final Answer:

• Average price: \(€7.50\)
• Average amount saved: \(€6.50\)