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Grade 12 · Science

Explain a design choice using stated priorities

Use a transparent weighted model to compare design tradeoffs and recognize that the choice depends on the priorities.

6 authored questions + worked example

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Worked example

Design A: performance 90, resource score 50. Design B: performance 70, resource score 80.

The stated rule is score = 6/10 × performance + 4/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

Answer & why

Answer: A tie under this scoring rule

A scores 6/10 × 90 + 4/10 × 50 = 74. B scores 6/10 × 70 + 4/10 × 80 = 74. This rule gives a tie under this scoring rule; changing the weights could change the decision.

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All questions

All 6 authored questions for this skill.

Question 1

Design A: performance 90, resource score 40. Design B: performance 70, resource score 70.

The stated rule is score = 4/10 × performance + 6/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

  1. Design A
  2. Design B
  3. A tie under this scoring rule
  4. There is not enough information to calculate the stated scores
A hint

Apply both weights to each design and compare totals; the result depends on the stated priorities.

Answer & why

Answer: Design B

A scores 4/10 × 90 + 6/10 × 40 = 60. B scores 4/10 × 70 + 6/10 × 70 = 70. This rule gives design b; changing the weights could change the decision.

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Question 2

Design A: performance 75, resource score 70. Design B: performance 80, resource score 40.

The stated rule is score = 8/10 × performance + 2/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

  1. There is not enough information to calculate the stated scores
  2. Design B
  3. A tie under this scoring rule
  4. Design A
A hint

Apply both weights to each design and compare totals; the result depends on the stated priorities.

Answer & why

Answer: Design A

A scores 8/10 × 75 + 2/10 × 70 = 74. B scores 8/10 × 80 + 2/10 × 40 = 72. This rule gives design a; changing the weights could change the decision.

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Question 3

Design A: performance 90, resource score 30. Design B: performance 60, resource score 80.

The stated rule is score = 3/10 × performance + 7/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

  1. There is not enough information to calculate the stated scores
  2. Design A
  3. Design B
  4. A tie under this scoring rule
A hint

Apply both weights to each design and compare totals; the result depends on the stated priorities.

Answer & why

Answer: Design B

A scores 3/10 × 90 + 7/10 × 30 = 48. B scores 3/10 × 60 + 7/10 × 80 = 74. This rule gives design b; changing the weights could change the decision.

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Question 4

Design A: performance 80, resource score 60. Design B: performance 60, resource score 80.

The stated rule is score = 5/10 × performance + 5/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

  1. Design B
  2. Design A
  3. There is not enough information to calculate the stated scores
  4. A tie under this scoring rule
A hint

Apply both weights to each design and compare totals; the result depends on the stated priorities.

Answer & why

Answer: A tie under this scoring rule

A scores 5/10 × 80 + 5/10 × 60 = 70. B scores 5/10 × 60 + 5/10 × 80 = 70. This rule gives a tie under this scoring rule; changing the weights could change the decision.

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Question 5

Design A: performance 90, resource score 50. Design B: performance 70, resource score 80.

The stated rule is score = 6/10 × performance + 4/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

  1. There is not enough information to calculate the stated scores
  2. A tie under this scoring rule
  3. Design A
  4. Design B
A hint

Apply both weights to each design and compare totals; the result depends on the stated priorities.

Answer & why

Answer: A tie under this scoring rule

A scores 6/10 × 90 + 4/10 × 50 = 74. B scores 6/10 × 70 + 4/10 × 80 = 74. This rule gives a tie under this scoring rule; changing the weights could change the decision.

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Question 6

Design A: performance 80, resource score 40. Design B: performance 65, resource score 90.

The stated rule is score = 7/10 × performance + 3/10 × resource score. Higher values are preferred for both measures. Which design has the higher score, or are they tied?

  1. There is not enough information to calculate the stated scores
  2. Design B
  3. A tie under this scoring rule
  4. Design A
A hint

Apply both weights to each design and compare totals; the result depends on the stated priorities.

Answer & why

Answer: Design B

A scores 7/10 × 80 + 3/10 × 40 = 68. B scores 7/10 × 65 + 3/10 × 90 = 72.5. This rule gives design b; changing the weights could change the decision.

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