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W e e k 1

In the first week, Lisa got 1 out of 5 problems correct whereas Bart got 5 out of 20 problems correct. In the second week, Lisa got 13 out of the remaining 25 problems correct, whereas Bart got 6 out of the remaining 10 problems correct. Lisa. Bart. 1 out of 5. 5 out of 20. W e e k 1.

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W e e k 1

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  1. In the first week, Lisa got 1 out of 5 problems correct whereas Bart got 5 out of 20 problems correct. In the second week, Lisa got 13 out of the remaining 25 problems correct, whereas Bart got 6 out of the remaining 10 problems correct.

  2. Lisa Bart 1 out of 5 5 out of 20 W e e k 1 13 out of 25 6 out of 10 W e e k 2 In the first week, Lisa got 1 out of 5 problems correct whereas Bart got 5 out of 20 problems correct. In the second week, Lisa got 13 out of the remaining 25 problems correct, whereas Bart got 6 out of the remaining 10 problems correct.

  3. Lisa Bart 1 out of 5 5 out of 20 W e e k 1 1 5 5 20 = 20% = 25% 13 out of 25 6 out of 10 W e e k 2 13 25 6 10 = 52% = 60%

  4. Lisa Bart 1 out of 5 5 out of 20 W e e k 1 1 5 5 20 = 20% = 25% 13 out of 25 6 out of 10 W e e k 2 13 25 6 10 = 52% = 60%

  5. 14 30 11 30 = 46.7% = 36.7% Lisa Bart 1 out of 5 5 out of 20 W e e k 1 1 5 5 20 = 20% = 25% 13 out of 25 6 out of 10 W e e k 2 13 25 6 10 = 52% = 60% 14 out of 30 11 out of 30 O v e r a l l

  6. 14 30 11 30 = 46.7% = 36.7% Lisa Bart 1 out of 5 5 out of 20 W e e k 1 1 5 5 20 = 20% = 25% 13 out of 25 6 out of 10 W e e k 2 13 25 6 10 = 52% = 60% 14 out of 30 11 out of 30 O v e r a l l

  7. Lisa Bart 1 out of 5 is 20% 5 out of 20 is 25% W e e k 1 How can you account forthis Surprising Phenomenon? 6 out of 10 is 60% 13 out of 25 is 52% W e e k 2 14 out of 30 is 46.7% 11 out of 30 is 36.7% O v e r a l l

  8. 20% 25% 52% 60% Lisa Bart 1 out of 5 is 20% 5 out of 20 is 25% W e e k 1 6 out of 10 is 60% 13 out of 25 is 52% W e e k 2 14 out of 30 is 46.7% 11 out of 30 is 36.7% O v e r a l l Why do we perceive Bart to do better? When we consider both weeks, our mind spontaneously does a simple average.

  9. Lisa Bart 20% 25% 1 out of 5 is 20% 5 out of 20 is 25% W e e k 1 52% 60% 6 out of 10 is 60% 13 out of 25 is 52% W e e k 2 Average of 20% and 52% is 36% Average of 25% and 60% is 42.5% 14 out of 30 is 46.7% 11 out of 30 is 36.7% O v e r a l l

  10. Lisa Bart 20% 25% When we use simple averaging, what happens the weight of each problem? 1 out of 5 is 20% 5 out of 20 is 25% W e e k 1 The problems in different weeks take different weights. 52% 60% 6 out of 10 is 60% 13 out of 25 is 52% W e e k 2 Average of 20% and 52% is 36% Average of 25% and 60% is 42.5% 14 out of 30 is 46.7% 11 out of 30 is 36.7% O v e r a l l

  11. Lisa Bart 20% 25% 1 out of 5 is 20% 5 out of 20 is 25% W e e k 1 Each item worths 5 pts Each item worths 20 pts 52% 60% 6 out of 10 is 60% 13 out of 25 is 52% W e e k 2 Each item worths 4 pts Each item worths 10 pts Average of 20% and 52% is 36% Average of 25% and 60% is 42.5% 14 out of 30 is 46.7% 11 out of 30 is 36.7% O v e r a l l Each item worths 3.33 pts Each item worths 3.33 pts

  12. Lisa Bart When we take simple average, the number of problems in each week are not taken into account. Since each problem has the same 3.33 points, we should give more weight to the week that has more problems. Contributes20 pts Contributes43.33 pts Contributes 30 pts Contributes 26 pts Contributes16.67 pts Contributes12.5 pts Contributes3.33 pts Contributes10 pts Average of 20% and 52% is 36% Average of 25% and 60% is 42.5% 14 out of 30 is 46.7% 11 out of 30 is 36.7% O v e r a l l

  13. Lisa 1 out of 5 W e e k 1 20% 13 out of 25 W e e k 2 52% We can compute Lisa’s overall score by using weighted average: Score = W1 0.20 + W2 0.52. What should the value of the weights W1 and W2?

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