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Learning Math Home
Data Session 9, Part A: Random Samples
 
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Session 9, Part A:
Random Samples

In This Part: Counting Penguins | Making Estimates

A possible sample might look like the one below. Let's explore how we might use the information in this sample to estimate the total number of penguins in the entire region.

Problem A1

Solution  

Suppose you had access to three samples: one with a single photo of one of the 100 sub-regions, one with photos of two sub-regions, and one with photos of three sub-regions. Use the results from each of these samples (pictured below) to make an estimate of the total number of penguins in the entire region (i.e., all 100 sub-regions).

Sample A: n = 1 (sample size = 1)

Sample B: n = 2 (sample size = 2)

Sample C: n = 3 (sample size = 3)

Record your counts and estimates in this table:

Sample

Photo 1

Photo 2

Photo 3

Estimate of Total

A

N/A

N/A

B

N/A

C

show answers


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


hide answers


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
In Samples B and C, you will need to use the sample results to make a "best guess" for the number of penguins in the entire region. What methods have you learned for coming up with such a guess?   Close Tip

 
 

In Problem A1, you may have determined a general rule for estimating the number of penguins in the entire population. One useful method is to find the mean of the counts in the sample and then multiply the mean by 100 (the number of sub-regions). Note 3


 

Problem A2

Solution  

Below is a sample of 10 sub-regions. Based on the number of penguins in this sample, make an estimate of the number of penguins in the entire region:


 
 

In making estimates by sampling, there is a balancing act in selecting the sample size. A larger sample size may cost more money or be more difficult to generate, but it should provide a more accurate estimate of the population characteristic you are studying. On the other hand, a sample size that is too small may not be accurate enough for you to be certain of your results.


Next > Part B: Selecting the Sample

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