# Central Limit Theorem Lab

Document Sample

```					Central Limit Theorem Lab                                                       Name:

The Central Limit Theorem says that under certain conditions, sample means of a certain size tend to
have a normal distribution. In this lab, you will simulate the following experiments:

    Rolling a pair of dice 50 times and finding the average of each roll
    Rolling five dice 50 times and finding the average of each roll
    Rolling twenty dice 50 times and finding the average of each roll

For each of these simulations, you will create a frequency distribution and histogram of your results.
Then you will compare the shape, center and spread of the distributions.

Collecting Averages of Pairs

1. In a blank data table, use StatCrunch and generate 50 rows with two columns. Data -> Simulate
Data -> Discrete Uniform. Enter the numbers you see below and press Simulate.

2. Find the average of each pair of dice rolls. Use Stat -> Summary Stats -> Rows and select the
Discrete Uniform 1 and Discrete Uniform 2 columns. Click Next. Deselect all of the statistics except
for Mean. Then click the checkbox next to “Store Output in Data Table.” Click Calculate.

You will see the mean for each pair of dice rolls in the third column titled Row Mean.

Adapted from: Mary Teegarden, "Central Limit Theorem: Central Limit Theorem Lab I (edited: Teegarden)," Connexions, August 12, 2008,
http://cnx.org/content/m17339/1.1/
3. Put the values into bins starting the bins at 1 and using a binwidth of 0.5. Use Data -> Bin Column.
Then fill in the values that you see below and click Calculate.

4. Construct a frequency table for the bin values by using Stat -> Tables -> Frequency and selecting
Bin(Row Mean). Click Calculate.

5. By hand, construct a histogram. Each bar should be 0.5 units wide. Each interval includes the left
endpoint but not the right endpoint. (For example, the interval from 1 – 1.5 includes all of the
numbers starting at 1 and up to but not including 1.5.)

6. Calculate the following for the 50 sample means using Stat -> Summary Stats -> Columns and then
select the Row Mean column. Click Calculate.

o    mean =
o    standard deviation =
o    sample size =

7. Draw a smooth curve through tops of the bars of the histogram.

Adapted from: Mary Teegarden, "Central Limit Theorem: Central Limit Theorem Lab I (edited: Teegarden)," Connexions, August 12, 2008,
http://cnx.org/content/m17339/1.1/
Collecting Averages of Groups of Five

1. In a blank data table, repeat steps 1 – 7 of the previous section and record the average value for
each of the 50 groups of 5 die tosses. Then create a frequency histogram of your results. Each bar
should be 0.5 units wide.

2. Calculate the following for the 50 sample means.

o    mean =
o    standard deviation =
o    sample size =

3. Draw a smooth curve through tops of the bars of the histogram.

Adapted from: Mary Teegarden, "Central Limit Theorem: Central Limit Theorem Lab I (edited: Teegarden)," Connexions, August 12, 2008,
http://cnx.org/content/m17339/1.1/
Collecting Averages of Groups of 20

1. Repeat steps 1 – 7 of the previous section and record the average value for each of the 50 groups of
20 die tosses. Then create a frequency histogram of your results. Each bar should be 0.5 units wide.

2. Calculate the following for the 50 sample means.

o    mean =
o    standard deviation =
o    sample size =

3. Draw a smooth curve through tops of the bars of the histogram.

Discussion Questions

1. As n increased, how did the shape of the distribution of the data change? Look at the curves that you
drew on your histograms and describe how the curves changed.

2. As n changed, how did the mean of the data change?

3. As n increased, how did the spread of the data change? (Hint: Compare the standard deviations.)

Adapted from: Mary Teegarden, "Central Limit Theorem: Central Limit Theorem Lab I (edited: Teegarden)," Connexions, August 12, 2008,
http://cnx.org/content/m17339/1.1/

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 20 posted: 8/13/2012 language: English pages: 4
How are you planning on using Docstoc?