random Sampling-statistics and probability

Guess the hidden
words using
images/emojis as
well as the clue
inside the box.
Game:
Guess the
Gibberish

Direction: The box will pass as the music
continues, and when it stops, the box also
stops. The person who holds it will have
the chance to pick his/her question, and
if it is blank, you are lucky that you don’t
have question to answer. (Each question
has a hint from the gibberish word.

Random Sampling
and Sampling
Distribution
Grade 11
Statistics and Probability
INSPIRED BY

illustrates random
sampling.
Learning Outcomes

Population
The set of all
possible value
of a variable
Sample
It consists of
one or more
data drawn from
population.

Activity: Sample and
Population!
Study the following and
identify the sample and
population in each situation.

A housewife buys a sack of rice.
She examined only a handful
of rice from the sack to find out
whether it is of good quality or
not.
Sample:
Population:

A housewife buys a sack of rice.
She examined only a handful
of rice from the sack to find out
whether it is of good quality or
not.
Sample: a
handful of
rice
Population:
a sack of
rice

Your mother wants to know
the taste of food she is
cooking or preparing. She
tasted only a spoonful of it.
Sample:
Population:

Your mother wants to know
the taste of food she is
cooking or preparing. She
tasted only a spoonful of it.
Sample: a
spoonful of
food
Population:
prepared
food

The teacher wants to know
the common height of OHS
student in Lala National
High School. She got only
10 OHS students from each
year level.
Sample:
Population:

The teacher wants to know
the common height of OHS
student in Lala National
High School. She got only
10 OHS students from each
year level.
Sample: OSH
students from
each year level
Population:
OSH students
in LNHS

Ramdom Sampling
Is a sampling method of
choosing representatives
from the population
wherein every sample has
an equal chance of being
selected.

Random Sample or Not
To determine the common
size of shoes her students
have, Mrs. Cruz draw her
sample from a box
containing the names of her
students with their shoe
sizes.
1.

Random Sample
To determine the common
size of shoes her students
have, Mrs. Cruz draw her
sample from a box
containing the names of her
students with their shoe
sizes.
1.

2. To know the common
size of the family her
classmates have, Julius
interviewed their class
officers.

Not a random sampling
2. To know the common
size of the family her
classmates have, Julius
interviewed their class
officers.

3. To determine the
performance of the SHS
students in Statistics, the
teacher draws 10 students
from every SHS class to
take the Statistics test.

Random Sample
3. To determine the
performance of the SHS
students in Statistics, the
teacher draws 10 students
from every SHS class to
take the Statistics test.

4. To determine the
most liked subject in
their school, Joel
interviewed the honor
students in each class.

4. To determine the
most liked subject in
their school, Joel
interviewed the honor
students in each class.
Not a random sampling

Different Type
of Random
Sampling

Simple Random Sampling
a sampling technique by
which every member of the
population has an equal
chance to be chosen as
sample.

Example:
When members of the population
of students have their names
represented into small pieces of
paper which are in the box then
mixed together and picked out at
random.

Systematic Sampling
which every member of the
population is selected with a
random start.
K= N/n (interval)

Example:
Imagine that you are all 60 in
a class. You really wanted to
draw 20 samples out of 60
students. So how are you
going to do it?

Example:
FORMULA:
k=N/n
k=60/20
k=3
Therefore, the interval
is 3.
Every 3rd students are
included as samples.
1,2,3,4,5,6,7,8,9,10,11,12,
…60

Stratified Random Sampling
is used when the population
can be classified into
groups based on some
characteristics such as age,
gender or socioeconomic
status.

Equal Allocation
Types of Stratified Random Sampling
This process chooses the
same number of
individuals or elements
from each group or
stratum, regardless of
their differences in size, to
form the sample

Equal Allocation
Types of Stratified Random Sampling
This process chooses the
same number of
from each group or
stratum, regardless of
their differences in size, to
form the sample
This process chooses
particular number of
proportional to the size
of each group or stratum
to form the sample.
Proportional
Allocation

EXAMPLE OF EQUAL ALLOCATION
Suppose a population is divided into
4 strata, A, B, C, and D, and you are
going to conduct a survey for your
research and you need 160
respondents (n). Let say A has a size
of 200, B with 300, C with 250, and
D with 250 as well.

EXAMPLE OF EQUAL ALLOCATION
STEP1: Divide the sample size by the
number of strata.
160÷4=40
STEP2: Select randomly a number of
40 individuals per stratum.
STEP3: Gather all 40 individuals from
each stratum to form the sample

EXAMPLE OF PROPORTIONAL ALLOCATION
Suppose a population is divided into
4 strata, A, B, C, and D, and you are
going to conduct a survey for your
research and you need 160
respondents (n). Let say A has a size
of 200, B with 300, C with 250, and
D with 250 as well.

STEP1: Add all the individuals per
stratum to determine the population
200+300+250+250=1000
STEP2: Divide the size of each stratum
with the population to determine their
proportions.
A=200÷1000=0.2 C=250÷1000=0.25
B=300÷1000=0.3 D=250÷1000=0.25

STEP3: Multiply each proportion
obtained from step 2 to the sample
size
A=0.2 ×160= 32
B=0.3 ×160= 48
C=0.25 ×160= 40
D=0.2 5×160= 40

Cluster Sampling
which the sample is taken
from different levels
generally from higher levels
to lower levels.

Example:
There are 14 clusters. After you
choose clusters randomly. You
can now choose in each
individuals to form your
sample.

Multi-Stage Sampling
a sampling technique
that is done using the
combination of different
sampling techniques

Types of Non-probability Sampling
Convenience Sampling - selecting
a sample based on the availability
of the member and/or proximity to
the researcher.
1.
Purposive Sampling - samples are
chosen based on the goals of study.
2.

Types of Non-probability Sampling
3. Snowball Sampling -
participants in the study were
tasked to recruit other members for
the study.

Solve the sample size.
GROUP A -500
GROUP B – 1300
GROUP C – 1600
GROUP D - 600

(RPS/N)n
where:
RPS= respondents
population size
Using Slovin’s Formula:
n=N/(1+Ne^2 )
where:
n = sample size
N = population size
e= margin error
e= 5% or 0.05

Presentation of Output:
Create a mind map, an
illustration or anything that will
describe and summarize the
assigned random sampling
technique.

Scenario
LNHS has 60 enrolled Grade 11
students. Maria, a Grade 12 student,
wants to conduct an interview on the
stressors of Grade 11 students and
how they manage their stress. She
wanted to interview ten (10) Grade 11
students. Help Maria select her
respondents.

1. Write the number of each
student in a piece of paper.
2. Roll the paper and put it in a
box.
3. Select your respondent by
drawing 10 pieces of paper in the box.
Group: Simple
random sampling

1. Arrange the name of students alphabetically.
2. Assign each student a number from 1 to 60.
3. Calculate your interval k by dividing the
population size by the sample size.
4. Select a number from the numbers 1 to k by drawing lots.
(write the number 1 to k in a piece of paper, and randomly
pick one. This is the number of your 1st respondent, which is
called the random start).
5. Choose every kth member from the random start as your
sample.
Group: Systematic sampling

Group the students by section.
1.
Calculate the no. of samples for each group
by proportional allocation.
2.
Write the names of each student in a piece of
paper, roll, put in a designated box per group
and randomly pick based on the computed
no. of samples per group.
3.
Group: Stratified random sampling

Group students by section.
1.
Write the name of each section in a
piece of paper and randomly pick 1.
2.
Select 10 students from that section
by means of simple random sampling.
3.
Group: Cluster sampling

Quiz
Determine the sample size required for the
given population using the Slovin’s Formula.
Find the sample size required using the
Slovin’s Formula from a population of 20,000
given a margin of error of 5%.
1.
Distribute the sample size obtained in number
1 as classified to the following categories:
2.

You have learned about the random sampling.
Please make sure to turn in your
assignment before the next session.
Good Job!

random Sampling-statistics and probability

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