Pink-Cute-Simple-Group-Project-Presentation_20250106_123703_0000.pdf

Statistics and probability

1. STATISTICS AND
PROBABILITY
QUARTER 3 – MODULE 4:
RANDOM SAMPLING, PARAMETER
AND STATISTIC, AND SAMPLING
DISTRIBUTION OF STATISTICS
STATISTICS AND
PROBABILITY
QUARTER 3 – MODULE 4:
RANDOM SAMPLING, PARAMETER
AND STATISTIC, AND SAMPLING
DISTRIBUTION OF STATISTICS

2. REPORTERSREPORTERS
Ashley B. AlbañoAshley B. Albaño Sheenliegh Love R. OliverSheenliegh Love R. Oliver

3. After going through this module, you are
expected to:
1. illustrate random sampling; (M11/12SP-IIId-2)
2. distinguish between parameter and statistic;
(M11/12SP-IIId-3) and
3. identify sampling distribution of statistics
(sample mean).(M11/12SP-IIId-4)
ObjectivesObjectives

4. The population refers to the whole group under study
or investigation. In research, the population does not
always refer to people. It may mean a group containing
elements of anything you want to study, such as objects,
events, organizations, countries, species, organisms, etc.
A sample is a subset taken from a population, either by
random sampling or by non-random sampling. A sample
is a representation of the population where it is hoped
that valid conclusions will be drawn from the population.

6. 0101
Lottery Sampling
add a little bit of body textTy
Types of Random Sampling Techniques
0202
Systematic Sampling
Stratified Random Sampling
0303
Random sampling is a selection of n elements derived from the N
population, which is the subject of an investigation or experiment,
where each point of the sample has an equal chance of being selected
using the appropriate sampling technique.

7. LOTTERYLOTTERY
SAMPLINGSAMPLING
- is a sampling technique in which each member of
the population has an equal chance of being
selected. An instance of this is when members of
the population have their names represented by
small pieces of paper that are then randomly mixed
together and picked out. In the sample, the
members selected will be included.

8. SYSTEMATICSYSTEMATIC
SAMPLINGSAMPLING
- is a sampling technique in which members of the
population are listed and samples are selected at
intervals called sample intervals. In this technique,
every nth item in the list will be selected from a
randomly selected starting point. For example, if
we want to draw a 200 sample from a population of
6,000, we can select every 3rd person in the list. In
practice, the numbers between 1 and 30 will be
chosen randomly to act as the starting point.

9. STRATIFIEDSTRATIFIED
RANDOMRANDOM
SAMPLINGSAMPLING
-is a sampling procedure in which members of the
population are grouped on the basis of their homogeneity.
This technique is used when there are a number of distinct
subgroups in the population within which full
representation is required. The sample is constructed by
classifying the population into subpopulations or strata on
the basis of certain characteristics of the population, such as
age, gender or socio-economic status. The selection of
elements is then done separately from within each stratum,
usually by random or systematic sampling methods.

10. Using stratified random sampling,
select a sample of 400 students
from the population which are
grouped according to the cities
they come from. The table shows
the number of students per city.
Example

11. To determine the number of
students to be taken as sample from
each city, we divide the number of
students per city by total population
(N= 28,000) multiply the result by
the total sample size (n= 400).
Solution

12. In this course, the parameters and statistics are
closely related terms that are important for the
determination of the sample size. Many have
trouble understanding the difference between
the parameter and the statistic, but it's important
to know exactly what these measures mean and
how to distinguish them.
Parameter and StatisticParameter and Statistic

13. A parameter is a descriptive population
measure. It is a measure of the characteristics
of the entire population (a mass of all the units
under consideration that share common
characteristics) based on all the elements
within that population.
What is Parameter?What is Parameter?

14. Examples of ParameterExamples of Parameter
1. All people living in one city, all-male
teenagers worldwide, all elements in a
shopping cart, and all students in a classroom.
2. The researcher interviewed all the students
of a school for their favorite apparel brand.

15. Statistic is the number that describes the sample. It
can be calculated and observed directly. The statistic
is a characteristic of a population or sample group.
You will get the sample statistic when you collect the
sample and calculate the standard deviation and the
mean. You can use sample statistic to draw certain
conclusions about the entire population.
What is Statistic?What is Statistic?

16. Examples of StatisticExamples of Statistic
1. Fifty percent of people living in the U.S.
agree with the latest health care proposal.
Researchers can’t ask hundreds of millions of
people if they agree, so they take samples or
part of the population and calculate the rest.
2. Researcher interviewed the 70% of covid-19
survivors

17. Sampling Distribution
of the Sample Means

18. A population consists of the five numbers 2, 3, 6, 10 and
12. Consider samples of size 2 that can be drawn from this
population.
A. How many possible samples can be drawn?
To answer this, use the formula NCn (the number of N
objects taken n at a time), where N is the total population
and n is the sample to be taken out of the population,
In this case N= 5 and n= 2
5C2 = 10
So, there are 10 possible samples to be drawn.

20. C. This time, let us make a probability distribution of the sample means.
This probability distribution is called the sampling distribution of the
sample means.
Observe that all sample
means appeared only
one; thus, their probability
is P(x)= 1/10 or 0.1

21. A sampling distribution of sample mean
is a frequency distribution using the
means computed from all possible
random samples of a specific size taken
from a population.

22. Construct a sampling distribution of sample mean for the set of
data below.
86 88 90 95 98
Consider a sample size of 3 that can be drawn from a
population.
A. How many possible samples can be drawn?
To answer this, use the formula NCn, where N is the total
population and n
is the sample to be taken out of the population,
In this case N= 5 and n= 3
5C3 = 10
So, there are 10 possible samples to be drawn.

23. B. Construct the sampling distribution of sample means

24. C. This time, let us make a probability distribution of the sample means.
This probability distribution is called, the sampling distribution of the
sample means.

25. THANK
YOU
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YOU
THANK
YOU
THANK
YOU