POPULATION & SAMPLE, PARAMETER &

STATISTIC AND SAMPLING TECHNIQUES

Lesson Objectives

At the end of this lesson, you are expected to:

1. Define and differentiate Population from Sample;

2. Distinguish between a Parameter and Statistics;
3. Illustrate Random Sampling;
4. Illustrate the other probability sampling techniques; and
5. Explain the different non-probability sampling
techniques.
Pre-Assessment

Check your readiness for this lesson by doing the

following activities. Determine the population and
sample.
1. Jade has 3 lollipops, Clint has 7 candies of red maxs.
How many candies are there?
2. There are 40 online students and 10 are offline students.
How many students in that class?
3. Inside the class there are 50 chairs, 30 usable wooden
chair, 15 are Plastic arm chair. How many are broken chair?

Red lines are sample, yellow lines are population.

 Population and Sample
Population

Sample

Population
- refers to the totality of observations or elements
from set of data.
Sample
- refers to one or more elements taken from
population for specific purpose.
Population and Sample
10 candies
7 red maxs

3 lollipops

50 students 50 chairs
5 broken, WC
10 offline

40 online 30 usable, WC 15 plastic, AC

 What I have learned So Far?
Identify whether the following examples refer to a
population or sample.
N/P a. The total number of students in a school.
n/S b. A group of 40 patients in a hospital who are given
particular treatment.
N/P c. The ages of all employees of a certain company.
n/S d. The top 50 tax payers in the Philippines.
N/P e. The list of all the countries in the world.
 Parameter VS Statistic
Parameter
- refers to a numerical measure that describes the
whole population.
All the students(230) in a school surveyed about the
heights and a weighted average height of 65 (in) was
determined, then 65 in is called the population
parameter.
 Parameter VS Statistic
Statistic
- refers to a numerical measure description of a
sample.
In the previous example, 65 in will be called the
sample statistic when only 50 of the students out of
230 students are surveyed to determine the
weighted average height of 65 (in)
 Parameter VS Statistic
Parameter
- we used the TOTAL DATA (Population) to get the
weighted average mean ( Population mean) in
describing the population.
Statistic
- we used the SPECIFIC DATA (Sample) from the
population to get the weighted average mean
(Sample Mean) in describing the sample.
 Identify the parameter and statistic used
in study.
1. The Food and Nutrition Research Institute of the Department of
Science and Technology (FNRI-DOST) surveyed 14 million Filipino adults
aged 20 and above and determined that 80% of the Filipino adults are
at risk of hypertension.
Solution:
What is our Population?
All Filipino adults age 20 and above at risk of hypertension.
Why not 14 million Filipino adults aged 20 and above are at risk of
hypertension?
- SAMPLE
The parameter is the percentage(100%) of all adults at risk for
hypertension out of all Filipino adults age 20 and above.
The statistic is the percentage of 80% obtained from the sample of 14
million adults.
 Identify the parameter and statistic used
in study.
2. A research wants to estimate the weighted average death age of
Filipino women in the last decade and from the sample of 100 deaths,
he obtained a sample mean age of 73.
Solution:
What is our Population?
All Filipino women who died in the last 10 years.
Why not 100 deaths of Filipino women in the last decade ?
- SAMPLE
The parameter is the weighted average death taken from the data of
all Filipino women who died in the last 10 years.
The statistic is the weighted average death age 73 identified from 100
samples.
 Identify the parameter and statistic used
in study.
3. Capvex is a drug used to treat patients with metastatic breast cancer. An
oncologist wants to determine the proportion of patients Capvex who are
healed within 10 weeks. A random sample of 300 breast cancer patients was
selected and 250 of them were healed after 10 weeks.
Solution:
What is our Population?
All patients with metastatic breast cancer who are healed within 10 weeks by
taking Capvex.
Why not 300 breast cancer patients who are healed within 10 weeks by taking
Capvex.?
- SAMPLE
The parameter is the proportion of patients Capvex who are healed within 10
weeks by taking it .
250
The statistic is the proportion = 0.833/83.33% obtained from the sample
300
of 300 patients who are healed within 10 weeks by taking it.
 What I have learned So Far?
Identify the parameter and statistic used in each of the following
situations.
1. A nutrition expert studies the modal height of teenagers and
from a sample of 70 teenagers, he concluded that the modal
height of teenagers is 165cm.
2. A population researcher computes the average number of
births per day and from a sample of 20 hospitals, he gathered
a mean of 100 births.
3. The Chief Executive Officer (CEO) of a tv network wants to
determine the median salary of his employees. Using a
random sample of 25 employees, he distinguished a median
salary of Php 35, 000.
 Answers
Identify the parameter and statistic used in each of the following
situations.
1. A nutrition expert studies the modal height of teenagers and
from a sample of 70 teenagers, he concluded that the modal
height of teenagers is 165cm.
Population, The height of all teenagers.
Sample, The height of 70 teenagers.
Parameter, The modal height of all teenagers.
Statistic, The modal height of 70 teenagers is 165cm.
 Answers
Identify the parameter and statistic used in each of the following
situations.
2. A population researcher computes the average number of
births per day and from a sample of 20 hospitals, he gathered a
mean of 100 births.
Population, The number of births per day from all hospitals.
Sample, The number of births per day from 20 hospitals.
Parameter, The average number of births per day from all
hospitals.
Statistic, The average number of births per day from 20 hospitals
is 100 births.
 Answers
Identify the parameter and statistic used in each of the following
situations.
3. The Chief Executive Officer (CEO) of a tv network wants to
determine the median salary of his employees. Using a random
sample of 25 employees, he distinguished a median salary of Php
35, 000.
Population, The salary of all employees.
Sample, The salary of 25 employees.
Parameter, The median salary of all employees.
Statistic, The median salary of 25 employees is Php 35, 000.
 Sampling Techniques
When conducting studies where only few members of the
population can participate, the selection of a sample is very crucial as
wrong sampling can lead to invalid results.
Two Categories in Sampling Techniques
Probability Sampling
- each member of the population has a known probability being
selected as sample.
Nonprobability Sampling
- there is bias in the selection and there is no recognized probability
that one member will be included in the sample.
Probability VS Nonprobability Sampling
- A sample is a small, representative part of the population. Samples
maybe selected from the population using probability (unbiased) or
nonprobability (biased) sampling.
 Probability Sampling Techniques
Simple Random Sampling
- Is the most commonly used sampling technique. In this technique,
each member of the population has an equal chance to be selected as
sample.
Naruto Elon Musk
Inuysha Billgates
Robin Rodrigo Duterte
Zoro Ezekiel Miller
Sakuragi Jack Ma
What is the probability we can
pick Ezekiel Miller from the urn?
1
10 = 0.10 =10%
 Probability Sampling Techniques
Simple Random Sampling
Inside the classroom with totals of 51 students and you are going to
pick your partner for research.

Naruto Elon Musk

Inuysha Billgates
Robin Rodrigo Duterte
Zoro Ezekiel Miller
Sakuragi Jack Ma
What is the probability you can point Jack
Ma to be your partner?
1
50 = 0.02 =2%
 Probability Sampling Techniques
Simple Random Sampling
Inside the classroom with totals of 100 students and you are going to
surveyed some of them for your study. How many samples you need to
get the best for your study?
To get the best number of sample to used.
Slovin’s Formula
𝑵
n= , where (n)sample size, (B) population size, (e) margin of error
𝟏+𝑵𝒆𝟐
e = 0.10 e = 0.05 e = 0.01
𝟏𝟎𝟎
n=
𝟏+𝟏𝟎𝟎(𝟎.𝟎𝟓)𝟐
𝟏𝟎𝟎 𝟏𝟎𝟎 𝟏𝟎𝟎
n= = =
𝟏+𝟏𝟎𝟎(𝟎.𝟎𝟎𝟐𝟓) 𝟏+(𝟎.𝟐𝟓) 𝟏.𝟐𝟓
n = 80 students needs to be survey for the study.
 Probability Sampling Techniques
Systematic Sampling
- is a random sampling technique which considers every nth element
of the population in the sample with selected random starting point
from the first q members.
Procedure:
1. Assign a number to each member of the population.
2. Choose a random starting point(n). This done by the dividing
number of members in the population by desired samples. The
quotient (q) will be skip count (q) members of the population from
starting point.
3. From Student n, skip count by q repeatedly until the desired
number of samples is completed. (SEPARATE the SELECTED ONES)
 Probability Sampling Techniques
Systematic Sampling
A sample of 10 will be selected from a population of 40 patients.
Procedure:
1. Assign a number to each member of the population.
2. Choose a random starting point(n). This done by the dividing number of
members in the population by desired samples. The quotient (q) will be skip
count (q) members of the population from starting point.
3. From Student n, skip count by q repeatedly until the desired number of samples
is completed. (SEPARATE the SELECTED ONES)
Solution:
1. P1, P2, P3……P40
𝑃𝑂𝑃𝑈𝐿𝐴𝑇𝐼𝑂𝑁
2. P3, desired sample (10 patients), 40 patients, skip count (q)= =
𝑁 40 𝐷𝐸𝑆𝐼𝑅𝐸𝐷 𝑆𝐴𝑀𝑃𝐿𝐸
= =4
𝑛 10
3. P3, P4, P5, P6, P7, P8, P9, P10,……P40
List all of Possible Samples =P3, P6, P9, P12, P15, P18, P21, P24, P27, P30, P33, P36,
P39
List all of Samples = P3, P6, P9, P12, P15, P18, P21, P24, P27, P30, P33, P36, P39
 Probability Sampling Techniques
Stratified Sampling
- sampling technique purposively divided into homogeneous partitions
(groups) depending on certain factors that might be affecting the
results of the study
- These homogenous partitions are called strata (singular: stratum).
A sample of 100 students is to be selected from a junior high school
population of 1000, which 250 are in grade 7, 200 are in grade 8, 300
are in grade 9 and 250 are in grade 10. If the sample size are is to be
proportionally distributed, how many samples are to be taken from
each other.
Given: G7 = 250, G8 = 200, G9 = 300 and G10 =250
250+200+300+250 = 1000 STUDENTS
Stratified Sampling
A sample of 100 students is to be selected from a junior high school
population of 1000, which 250 are in grade 7, 200 are in grade 8, 300
are in grade 9 and 250 are in grade 10. If the sample size are is to be
proportionally distributed, how many samples are to be taken from
each other.
Given: G7 = 250, G8 = 200, G9 = 300 and G10 =250

Partitions Size of the Partition Number of Samples

Grade 7 250 250
x100 = 25
1000
Grade 8 200 200
x100 = 20
1000
Grade 9 300 300
x100 = 30
1000
Grade 10 250 250
x100 = 25
1000
Total 1000 100
Stratified Random Sampling
A sample of students is to be selected from a junior high school
population of 1000, which 250 are in grade 7, 200 are in grade 8, 300
are in grade 9 and 250 are in grade 10. If the sample size are is to be
proportionally distributed, how many samples are to be taken from
each other.
𝑵 𝟏𝟎𝟎𝟎 𝟏𝟎𝟎𝟎 𝟏𝟎𝟎𝟎 𝟏𝟎𝟎𝟎
n= = = = = =285.7 = 286
𝟏+𝑵𝒆𝟐 𝟏+𝟏𝟎𝟎𝟎(𝟎.𝟎𝟓)𝟐 𝟏+𝟏𝟎𝟎𝟎(𝟎.𝟎𝟎𝟐𝟓) 𝟏+𝟐.𝟓 𝟑.𝟓

Partitions Size of the Partition Number of Samples

Grade 7 250 250
x286 = 71.5 = 72
1000
Grade 8 200 200
x286 = 57.2 = 57
1000
Grade 9 300 300
x286 = 85. 8 = 86
1000
Grade 10 250 250
x286 = 71.5 = 71
1000
Total 1000 286
 Probability Sampling Techniques
Stratified Sampling
Note:
Stratified random Sampling is particularly useful only in conditions
when the population is divided into homogeneous groups.
The members are grouped similarly based on controlling variable in the
study such as gender, race, civil status or nationality.
 Probability Sampling Techniques
Cluster Sampling
- the population is divided into partitions (groups), called as cluster.
- However, unlike stratified sampling, clusters are heterogenous
groups of population.
- This means they are grouped differently according to the controlling
variables in the study.
- The sample is taken through a random selection of clusters and all
members in that cluster will be the sample.
A sample of students is to be selected from a junior high school
population of 1000, which 250 are single, 200 are foreigner, 300 are
male and 250 are dark skinned. If the sample size are to be taken from
the groups of single , how many samples are there?
SINGLE FOREIGNER D - SKINNED MALE TOTAL
SAMPLE 250 200 250 300 1000
 Nonprobability Sampling Techniques
Convenience Sampling
Haphazard Sampling
- as the name implies, this sampling procedure s carried out on the
matter of convenience or ease of implementation on the part of
researcher, the samples are taken readily available to participate int
the study.
- Ambush Interview
- Opinion Poll
Purposive Sampling
- this sampling is done with the purpose in mind.
- this technique, also known as judgmental or selective sampling,
focuses on sample which are taken based on the judgment of the
researcher.
- Dr., Master, Experts to that certain Fields.
 Nonprobability Sampling Techniques
Snowball Sampling
- sometimes called chain-referral sampling.
- the researcher chooses a positive respondent for a study at hand.
Then each respondent is ask to give recommendations or referrals to
other possible respondents.
- FRONT ROW, UNO
Quota Sampling
- equivalent of stratified random sampling in terms of nonprobability
sampling.
- the researcher starts by identifying quotas, which are predefined
control categories such as age, gender, education, religion, and etc.
The first 30 students got inside the class will be the samples out the
entire students in that class.
What I have learned So Far?
Identify sampling technique illustrated in the following
scenarios.
1. Kyle chose 10 samples from population of 50 by assigning numbers to
each member and then selecting the members whose assigned
numbers are multiples of 5. Systematic Sampling
2. A researcher grouped the respondents according to religious
affiliation and choose proportional numbers of members from each
religious group. Stratified Sampling
3. A teacher assign class numbers to each student and then spun a
number roulette to identify the members of sample.
Simple Random Sampling
4. A researcher whose studies the effectiveness of a particular drug
chose four hospitals at random which are located within the region and
then surveyed all the patients in selected hospitals. Cluster Sampling
5. A company executive selected 15 participants for the international
business congress by writing the names of all employees and then
choosing a name one at a time until delegation is completed.Purposive
What I have learned So Far?
Identify sampling technique illustrated in the following
scenarios.
6. John conducted an online survey about mostly preferred
presidential candidate. Purposive Sampling/ Snowball
7. Annie asked some respondents to suggest other possible
participants for the research. Snowball Sampling
8. The researcher grouped together the members of the
population into categories and then choose possible respondents
from each category. Convenience Sampling
9. The teacher chose the top three students of the batch to
represent the school in a regional quiz show. Quota/Con/Pur
10. Differentiate probability sampling from nonprobability
sampling techniques.