Statistics and probability 11

1. Sampling Distribution
of the Sample Mean
1

2. Is a frequency distribution using
the means computed from all
possible random samples of a
specific size taken from a
population. The means of the
samples are less than or greater
than the mean of the population.
SAMPLING DISTRIBUTION OFSAMPLE MEANS
2

3. 1. Determine the number sets of
all possible random samples that
can be drawn from the given
population by using the formula,
, where N is the population size
and n is the sample size.
STEPSINSAMPLING DISTRIBUTION OFSAMPLE MEANS
3
N n
C

4. 2. List all possible samples and
compute the mean of each
sample.
3. Construct a sampling
distribution.
4. Construct histogram of the
sampling distribution.
STEPSINSAMPLING DISTRIBUTION OFSAMPLE MEANS
4

5. A population of Senior High School
consists of numbers 1, 2, 3, 4, 5. Create a
sampling distribution of size 3.
EXAMPLE
5

6. 1. Determine the number sets of all possible random
samples that can be drawn from the given
population by using the formula, , where N is the
population size and n is the sample size.
2. List all possible samples and compute the mean of
each sample.
6
N n
C
!
!( )!
N n
N
C
n N n


SOLUTION

7. 7
SOLUTION

8. 3. Construct a frequency and probability distribution table
of the sample means indicating its number of occurrences
or the frequency and probability.
8
SOLUTION

9. 4. Construct histogram of the sampling distribution.
9
SOLUTION

10. How many different samples of size n can be obtained
from the following population N sizes?
10
Independent Practice

11. A population consists of the values (1, 4, 3, 2). Consider
samples of size 2 that can be drawn from this population.
a. List down all the possible samples and corresponding
sample mean
11
Independent Practice

12. A population consists of the values (1, 4, 3, 2). Consider
samples of size 2 that can be drawn from this population.
b. Construct the sampling distribution of the sample
means.
12
Independent Practice

13. 1. What distribution pertains to the
frequency distribution of the sample
mean from all the possible random
samples of a particular sample size n
taken from the given population?
a. frequency c. population
b. normal d. sampling
13
QUIZ

14. 2. Which of the following is NOT a step in
creating sampling distribution of the sample
mean?
a. Compute for the standard deviation and variance of the
samples.
b. Construct a frequency distribution table of the sample
means and probability.
c. Determine the number of sets of all possible random
samples.
d. List all the possible random samples and solve for the
sample mean of each set of samples.
14
QUIZ

15. 3. Which of the following is the mean of
sample 6, 10, 21, 25, and 28?
a. 15.17
b. b. 18
c. c. 21.2
d. d. 22
15
QUIZ

16. For numbers 4-5, refer to the following set of
data of a population {11, 12, 13, 14}.
4. How many different samples of size n = 2 can
be drawn from the population?
a. 6
b. 5
c. 4
d. 3
16
QUIZ

17. For numbers 4-5, refer to the following set of
data of a population {11, 12, 13, 14}.
5. What is the lowest value of the sample mean
in this sampling distribution?
a. 11.5
b. b. 12
c. c. 12.5
d. d. 13
17
QUIZ

18. Loren was able to sell several pairs of Marikina
shoes that have sizes of 4, 5, 6, 7,
and 8. Consider samples of size 3 that can be
drawn from this population.
18
ACTIVITY

19. 19
ACTIVITY