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Learning Math Home
Data Session 9: Solutions
 
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Solutions for Session 9, Part A

See solutions for Problems: A1 | A2


Problem A1

Sample A:
This sample of one sub-region shows five penguins:

Based on this limited information, you might guess that each and every sub-region contains five penguins. Since there are 100 sub-regions, your estimate of the total number of penguins would be 100 x 5 = 500.

Sample B:
This sample of two sub-regions contains 5 + 6 = 11 penguins, or an average of 11/2 penguins per sub-region:

Based on this limited information, you might guess that the average for all 100 sub-regions is 11/2 penguins. Since there are 100 sub-regions, your estimate of the total number of penguins would be 100 x (11/2) = 550.

Sample C:
This sample of three sub-regions contains 5 + 6 + 3 = 14 penguins, or an average of 14/3 penguins per sub-region:

Based on this limited information, you might guess that the average for all 100 sub-regions is 14/3 penguins. Since there are 100 sub-regions, your estimate of the total number of penguins would be 100 x (14/3) = 1,400/3, or, to the nearest penguin, 467 penguins.

Here is the completed table:

Sample

Photo 1

Photo 2

Photo 3

Estimate of Total

A

5

N/A

N/A

500

B

5

6

N/A

550

C

5

6

3

467

<< back to Problem A1


 

Problem A2

First, find the average number of penguins in each sub-region of the sample. The total number of penguins is 5 + 6 + 6 + 7 + 5 + 2 + 1 + 5 + 5 + 3 = 45. Since there are 10 sub-regions in the sample, the average number of penguins is 45/10. Therefore, a good estimate for the total number of penguins is 100 x 45/10 = 450 penguins.

<< back to Problem A2


 

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