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Compare average unit profit under mix shift

Capital OneData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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This question tests the candidate's ability to calculate weighted averages and understand how changes in sales volume distribution (mix shift) affect the overall average profit per unit.

Scenario

You are analyzing a product line for an e-commerce company that sells two items: a 'Basic' model and a 'Premium' model.

  • The Basic model sells for $50 with a profit margin of $10.
  • The Premium model sells for $150 with a profit margin of $40.

In January, the company sold 800 units of the Basic model and 200 units of the Premium model. In February, the company sold 500 units of the Basic model and 500 units of the Premium model.

Task

  1. Calculate the average profit per unit for January and February separately.
  2. Explain why the average profit per unit changed between the two months, even though the profit margin for each individual product remained constant.
  3. Determine what the total profit would have been in February if the sales mix had remained identical to the January ratio (maintaining the total number of units sold in February).

Example

If you sell 1 unit at $10 profit and 1 unit at $20 profit, your average profit per unit is ($10 + $20) / 2 = $15.

Hints

Hint 1

Recall that the weighted average is the sum of (value * weight) divided by the total count.

Hint 2

Observe how the increase in the proportion of the higher-margin 'Premium' units shifts the overall average toward the higher profit value.

Hint 3

To solve the third task, calculate the total units sold in February (1,000) and apply the percentage share of products from January (80% Basic, 20% Premium) to that total.

Follow-up questions

  • How would a significant increase in marketing costs for the Basic model, which reduces its individual unit profit by $5, affect the overall average profit?
  • If we introduce a third product, 'Deluxe', how would its inclusion change our methodology for tracking mix shift?
  • Can you describe a scenario where total revenue increases while total average profit per unit decreases?