Statistics and Probability

1. STATISTICS & PROBABILITY
MS. DIVINA B. BERNALDEZ, LPT

2. SAMPLING
is the process of selecting a small
number of elements from a larger
defined target group of elements.

3. SAMPLING
is the process of selecting a small
number of elements from a larger
defined target group of elements.

4. POPULATION SAMPLE
• 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.

5. POPULATION SAMPLE
• 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. POPULATION SAMPLE
Examples:
• the population of senior
citizens in Metro Manila
• the population of students in
the senior high school
program
• Filipino Families affected
financially by the pandemic.
Examples:
• a sample of 500 senior
citizens from Metro Manila
• a sample of 1000 grade 11
students from Metro Manila
• 5 million Filipino Families are
financially affected by the
pandemic.

7. PARAMETER STATISTICS
• describes an entire
population.
• refers to the numerical
measure of population.
• describes only the sample
• refers to the numerical
measure of the sample.
• 𝜇 for the population mean
• 𝜎2
for the population
variance.
• 𝑋 for the sample mean
• 𝜎2
for the sample variance

8. Identify the parameter and/or statistic in the following situations:
1.Twenty-five out of the 100 randomly chosen grade 11 students belong
to STEM strand.
2. A group of social workers surveyed 5 million Filipino families and
determined that 82% of Filipino families are affected by the pandemic.
3. All SHS students in a school are surveyed about their weights, and
an average weight of 118 pounds was determined.
4. The university claims that on average, it takes at least 30 minutes to
find a parking space on the campus.
5. Suppose the data report shows that, for the past 5 years, the
average score of Grade 6 pupils in the National Achievement Test is

9. Identify the parameter and/or statistic in the following situations:
1.Twenty-five out of the 100 randomly chosen grade 11 students belong
to STEM strand.
2. A group of social workers surveyed 5 million Filipino families and
determined that 82% of Filipino families are affected by the pandemic.
3. All SHS students in a school are surveyed about their weights, and
an average weight of 118 pounds was determined.
4. The university claims that on average, it takes at least 30 minutes to
find a parking space on the campus.
5. Suppose the data report shows that, for the past 5 years, the
average score of Grade 6 pupils in the National Achievement Test is

10. PROBABILITY
SAMPLING
NON-PROBABILITY
SAMPLING
Every element in a
population has a chance of
being selected and that
chance can be quantified.
• Applied if every element in
a population does not have
equal chance of being
selected.
• Rely upon convenience and
access, assurance that
participants fit
characteristics or referrals
of others with like
characteristics.

11. PROBABILITY
SAMPLING
NON-PROBABILITY
SAMPLING
Every element in a
population has a chance of
being selected and that
chance can be quantified.
• Applied if every element in
a population does not have
equal chance of being
selected.
• Rely upon convenience and
access, assurance that
participants fit
characteristics or referrals
of others with like
characteristics.

12. Samples are chosen to reflect the characteristics of the
population. Individuals or members of sample are selected
according to the different random sampling methods.
 Simple Random Sampling
 Systematic Random Sampling
 Stratified Random Sampling
 Cluster Random Sampling

13.  Involves selecting a sample size (n) from a population size (N)
so that all elements of the population have equal chances of
being a part of the sample.
 The process is done by choosing the sample one by one, using
either lottery or table of random numbers, or using automatic
random number generators (like in Microsoft Excel).
Examples:
• The teacher writes all the names of students in a piece of
paper and puts it in a box for the graded recitation.
• From the list containing the names of 300 members of a
certain networking business, a sample size of 75 obtained by
using automatic generator in Microsoft Excel.
SIMPLE RANDOM SAMPLING

14.  Involves selecting a sample size (n) from a population size (N)
so that all elements of the population have equal chances of
being a part of the sample.
 The process is done by choosing the sample one by one, using
either lottery or table of random numbers, or using automatic
random number generators (like in Microsoft Excel).
Examples:
• The teacher writes all the names of students in a piece of
paper and puts it in a box for the graded recitation.
• From the list containing the names of 300 members of a
certain networking business, a sample size of 75 obtained by
using automatic generator in Microsoft Excel.
SIMPLE RANDOM SAMPLING

15.  Involves selecting a sample using a random starting point, and
then drawing successive elements from the target population.
In short you pick every nth interval from the target population.
Examples:
• The teacher gets the class record and call every 4th name in
the list.
• Every five files out of 500 files will be chosen.
• Condo units in a certain city appear to have an area of 25
square meters in every 5th floor. Enumerator from the
municipality office was asked to visit households living in the
same area of condo units.
SYSTEMATIC RANDOM SAMPLING

16.  Involves selecting a sample using a random starting point, and
then drawing successive elements from the target population.
In short you pick every nth interval from the target population.
Examples:
• The teacher gets the class record and call every 4th name in
the list.
• Every five files out of 500 files will be chosen.
• Condo units in a certain city appear to have an area of 25
square meters in every 5th floor. Enumerator from the
municipality office was asked to visit households living in the
same area of condo units.
SYSTEMATIC RANDOM SAMPLING

17.  a sampling procedure in which members of the population are
grouped on the basis of their homogeneity.
 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.
 Example:
• According to the office of Senior Citizens Affairs (OSCA), as of
year 2015 there are 118, 222 Filipino senior citizens living in
Manila. A sample of 1,000 Filipino senior citizens is to be
selected according to its gender as presented in the table.
STRATIFIED RANDOM SAMPLING

18.  a sampling procedure in which members of the population are
grouped on the basis of their homogeneity.
 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.
 Example:
• According to the office of Senior Citizens Affairs (OSCA), as of
year 2015 there are 118, 222 Filipino senior citizens living in
Manila. A sample of 1,000 Filipino senior citizens is to be
selected according to its gender as presented in the table.
STRATIFIED RANDOM SAMPLING

19. Gender Size
Percentage of
Distribution
Number of
samples
Male 48, 855
48,855
118, 222
× 100% = 41% 41% × 1, 000 = 410
Female 69,367
69,367
118, 222
× 100% = 59% 59% × 1,000 = 590
Total 118, 222 100% 1,000
Thus, a sample of 1,000 Filipino senior citizens living in Manila
will consist of 410 males and 590 females.

20.  Cluster sampling is sometimes referred to as area
sampling and applied on a geographical basis.
 Generally, first sampling is performed at higher
levels before going down to lower levels.
 For example, samples are taken randomly from
the provinces first, followed by cities,
municipalities or barangays, and then from
households
CLUSTER RANDOM SAMPLING

21.  Cluster sampling is sometimes referred to as area
sampling and applied on a geographical basis.
 Generally, first sampling is performed at higher
levels before going down to lower levels.
 For example, samples are taken randomly from
the provinces first, followed by cities,
municipalities or barangays, and then from
households
CLUSTER RANDOM SAMPLING

22.  Cluster sampling is sometimes referred to as area
sampling and applied on a geographical basis.
 Generally, first sampling is performed at higher
levels before going down to lower levels.
 For example, samples are taken randomly from
the provinces first, followed by cities,
municipalities or barangays, and then from
households
CLUSTER RANDOM SAMPLING

23. A. Identify the parameter and statistic in each of the following.
1. A researcher wants to determine the monthly average amount
of pension receiving by the senior citizens in Manila. From a
random sample of 50 senior citizens, an average pension
amounting to 4,500 was determined.
2. Hotel manager surveys the mean age of employees in the past
five years from 100 employees, a mean age of 28.4 is
identified.
3. With an average IQ of 86 points, the Philippines runs 10th place
in the smartest countries in ASEAN.
4. From 3.18Mbps previously to 18.35Mbps, the latest insight
ranked the Philippines 111th from its mobile speeds as of
ASSIGNMENT

24. C. Classify the random sampling method illustrated in the
following situations.
1. A teacher assigned class numbers to each student, and she
used a number spinning wheel to identify the members of the
sample.
2. Barangay security members were selected according to
whether they prefer day or night duties.
3. Every 10th motorist is selected passing through EDSA to
determine his or her speed.
4. Select the residents in a certain municipality according to the
following types of occupation: blue-collar workers, OFW, and
professionals.
ASSIGNMENT

25. 5. Rafael chose 15 samples from the population of 100 by
assigning numbers to each member, and then selecting
the members whose assigned numbers are multiples of 6.
6. Using a random number generator, select the sample of
75 from the population.
7. A researcher wants to conduct a study to determine the
performance of law students in the Philippines.
8. Suppose that ten boxes of items are numbered 1 to 10.
A fixed number will then drawn randomly from the bowl to
obtain the sample for some kind of testing.
ASSIGNMENT

26. 9. Athletes participating in the Olympic games for the past 10 years to
obtain their rate of performance.
10. Choose three sections from among the 10 sections of Grade 11
students in a certain school.
ASSIGNMENT

27. C. Get the samples needed for each category using stratified random
sampling. There are 20 members of taekwondo club, 40 math club
members, 60 drama theatre members, and 30 members of science
club. The researchers want to get 20 respondents out of these
organizations. Identify the samples to be taken in each organization.
ASSIGNMENT

28. THANK YOU