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Learning Math Home
Data Session 9, Part D: The Effect of Sample Size
 
Session 9 Part A Part B Part C Part D Homework
 
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Session 9, Part D:
The Effect of Sample Size

In This Part: Sample Size 20 | Comparing Sample Sizes 10 and 20 | Box Plot Comparisons

In the previous discussion, you investigated how increasing the sample size does two things:

 

Decreases the sample-to-sample variation in the estimates

 

Produces a higher proportion of estimates closer to the actual population size

We can also use another familiar method to explore this phenomenon: the Five-Number Summary and box plot.


 

Problem D3

Solution  

Here is the stem and leaf plot for the 100 estimates from samples of size 10:

Use the stem and leaf plot to determine the Five-Number Summary for these estimates. These questions may help you along:

a. 

What is the position of the median, and which two values are used to calculate it?

b. 

If there are 50 values in each half, how are the quartiles calculated?

c. 

Complete the Five-Number Summary table:


 

Sample Size 10

Maximum

Upper Quartile (Q3)

Median

Lower Quartile (Q1)

Minimum

show answers

 

 

Sample Size 10

Maximum

620

Upper Quartile (Q3)

540

Median

500

Lower Quartile (Q1)

470

Minimum

360

hide answers


 

Problem D4

Solution  

Generate the Five-Number Summary for this stem and leaf plot of the 100 estimates based on samples of size 20:

 

Sample Size 20

Maximum

Upper Quartile (Q3)

Median

Lower Quartile (Q1)

Minimum

show answers

 

 

Sample Size 20

Maximum

610

Upper Quartile (Q3)

530

Median

500

Lower Quartile (Q1)

482.5

Minimum

390

hide answers


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Since the number of estimates is the same as Problem D3's, the quartiles and median will be in the same positions. Count the values in increasing order to find them.   Close Tip

 

Problem D5

Solution  

Create two box plots for the Five-Number Summaries you generated in Problems D3 and D4, placing them side by side on the same scale to make them easier to compare.


 

Problem D6

Solution  

What do the box plots suggest about the effect of sample size on the accuracy of the estimates? In particular, how do the box plots illustrate the following:

a. 

How much the estimates vary from sample to sample

b. 

How close the estimates are to the actual value of 500



video thumbnail
 

Video Segment
In this video segment, the participants discuss what percentages of their data fell in particular interval ranges for samples of size 10 and 20. Professor Kader then introduces the Central Limit Theorem to further discuss the connection between probability and statistics. What is the give-and-take between selecting an interval range and sample size when designing a statistical investigation? How would you use this information to plan a statistical investigation? How can you be more precise when taking a sample size? How can you be more accurate?

If you're using a VCR, you can find this segment on the session video approximately 16 minutes and 2 seconds after the Annenberg Media logo.

 

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