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

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

Sample Size 10

 Maximum 620 Upper Quartile (Q3) 540 Median 500 Lower Quartile (Q1) 470 Minimum 360

Problem D4

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

Sample Size 20

 Maximum 610 Upper Quartile (Q3) 530 Median 500 Lower Quartile (Q1) 482.5 Minimum 390

 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 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

 Problem D5 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

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 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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 Session 9: Index | Notes | Solutions | Video