2. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
illustrate random sampling;
distinguish between parameter
and statistic; and
construct sampling distribution of
sample means.
Objectives
3. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Constructing Frequency Distribution
The following are the blood types of a group of
individuals in a government office. Construct a
frequency distribution for the different blood types
4. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Constructing Frequency Distribution
x f
A 5
B 7
O 9
AB 4
5. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
•You have learned in your previous
lessons how to construct frequency
distribution and probability
distribution. In this lesson, you will
learn how to construct sampling
distribution of the sample means.
6. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Computing for the mean of a Sample
Find the mean of the following sets numbers
7. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Combination
A combination is a mathematical technique
that determines the number of possible
arrangements in a collection of items where the
order of the selection does not matter. In
combinations, you can select the items in any
order.
8. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Combination of N objects
Taken r at a time.
The number of samples of size r that can be
drawn from a population of size N is given by NCn.
𝑛𝐶𝑟 =
𝑛!
𝑟!(𝑛−𝑟)!
Where:
n = size of the population
r = size of the sample
9. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Evaluating Combination of N objects
Taken n at a time.
1. 4C2
2. 6C4
3. 6C3
4. 10C4
=
𝑁!
𝑛!(𝑁−𝑛)!
=
4!
2!(4−2)!
=
4!
2!(2)!
=
4 3 2!
2!2!
=
12
2
= 𝟔
=
𝑁!
𝑛!(𝑁−𝑛)!
=
6!
4!(6−4)!
=
6!
4!(2)!
=
6(5)(4!)
4!2!
=
30
2
= 𝟏𝟓
=
𝑁!
𝑛!(𝑁−𝑛)!
=
6!
3!(6−3)!
=
6!
3!(3)!
=
6(5)(4)(3!)
3!3!
=
6 5 (4)
3(2)(1)
= 𝟐𝟎
=
𝑁!
𝑛!(𝑁−𝑛)!
=
10!
4!(10−4)!
=
10!
4!(6)!
=
10(9)(8)(7)(6!)
4!6!
=
10(9)(8)(7)
4(3)(2)(1)
= 𝟐𝟏𝟎
10. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Evaluate the following.
1. 5𝐶3
2. 8𝐶4
3. 9𝐶6
4. 10𝐶3
5. 12𝐶8
11. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
•Researchers use sampling if taking
a census of the entire population is
impractical. Data from the sample
are used to calculate statistics,
which are estimates of the
corresponding population
parameters.
12. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
•Descriptive measures computed
from a population.
13. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
•Descriptive measures computed
from a sample.
14. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Sampling Distribution of Sample Means
• The number of samples of size r that can be
drawn from a population of size N is given by NCr.
• A sampling distribution of sample means is a
frequency distribution using the means computed
from all possible random samples of a specific
size taken from a population.
• The probability distribution of the sample means
is also called the sampling distribution of the
sample means.
15. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Steps in Constructing the Sampling
Distribution of the Means
1. Determine the number of possible samples that can be
drawn from the population using the formula: NCr
where N = size of the population r = size of the
sample
2. List all the possible samples and compute the mean of
each sample.
3. Construct a frequency distribution of the sample
means obtained in Step 2.
16. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Example
A population consists of the numbers 2, 4,
9, 10, and 5.
a. List all possible samples of size 3 from
this population.
b.Compute the mean of each sample.
c. Prepare a sampling distribution of the
sample means.
17. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Solution to Example 1a
The possible
samples of size
3 from 2, 4, 9,
10, and 5 are…
18. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Solution to Example 1b
The mean of each sample are as follows:
19. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Solution to Example 1c
The sampling distribution of the sample
means
20. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Exercise
A group of students got the following scores in
a test: 6, 9, 12, 15, 18, and 21. Consider
samples of size 3 that can be drawn from this
population.
a. List all the possible samples and the
corresponding mean.
b. Construct the sampling distribution of the
sample means.
21. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Exercise 1
Samples of three cards are drawn at
random from a population of eight cards
numbered from 1 to 8.
a. How many possible samples can be
drawn?
b.Construct the sampling distribution of
sample means.
22. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Exercise 3
A finite population consists of 8 elements.
10, 10, 10, 10, 10, 12, 18, 40
a. How many samples of size n = 2 can be drawn
from this population?
b. List all the possible samples and the
corresponding means.
c. Construct the sampling distribution of the
sample means.
23. L i b e r a t i n g N e t w o r k i n E d u c a t i o n
Thank you!
