Download Sampling Distribution of the Sample Means

Math 11 – Group Work
Central limit Theorem
Names___________________________
Sampling Distribution of the Sample Means
100 samples of size 30 were collected from the population of student heights from the Census at
School data (Student heights from the population of Grade 11 students across NS). Below are the
average heights (mean height) for the 100 samples. The population these samples were taken
from was N(169.4, 12.3)
177.2
168.4
174.6
168.2
171.3
168.3
171.4
169.6
168.2
171.6
170.2
168.0
174.5
168.0
174.1
168.4
169.9
167.9
172.4
169.8
168.9
170.1
172.7
170.8
169.1
167.9
172.7
167.9
170.0
169.6
170.8
167.8
167.7
170.7
167.6
170.6
171.7
169.0
167.7
170.8
167.5
172.9
168.8
170.1
174.0
167.3
170.6
168.4
172.7
169.9
169.4
167.2
169.8
167.2
172.4
169.5
168.7
170.4
167.2
171.7
169.3
172.4
168.5
166.8
170.7
170.1
173.7
169.4
170.7
169.0
166.8
173.0
166.6
173.1
169.9
166.5
170.7
166.4
170.4
169.4
169.4
171.7
169.8
166.1
170.3
165.8
170.2
168.7
173.5
169.3
170.0
169.8
168.5
169.7
173.3
165.8
173.4
165.6
169.9
169.1
Put this data into a list in your calculator. Create a histogram with the window
shown at right. Use the trace button to complete the frequency table from your
histogram. Draw the histogram of the sample means on the grid below – this is
called the sampling distribution. Determine the mean of your list (the mean of
the sample means) and the standard deviation of your list (the standard
deviation of the sample means) and record them below.
Sample Mean
164-165
165-166
166-167
167-168
168-169
169-170
170-171
171-172
172-173
173-174
174-175
175-176
Frequency
Mean of the sample means _________
Std dev of the sample means _______
Math 11 – Group Work
Central limit Theorem
Names___________________________
Record:
• the mean of the sample means_____
• the “population” mean_______
Record:
•
•
the standard deviation of the sample means_____
the “population” standard deviation_____
Points to Ponder
1. Does it appear that the histogram created is approximately normal? Explain.
2. How do the means compare? Explain.
3. How do the standard deviations compare? Explain.
4. Divide the population standard deviation by
n , where n is the sample size.
5. How does the answer above compare with the standard deviation of the sampling
distribution (the std dev of the sample means)?
6. What do you think would happen to the standard deviation of the sampling distribution if a
larger sample size was taken? Explain.