Math11 SP Q3 M5 PDF
Math11 SP Q3 M5 PDF
Math11 SP Q3 M5 PDF
Department of Education
Regional Office IX, Zamboanga Peninsula
What I Know
2. What type of sampling technique where each list of elements in the population is used as a
sampling frame and the element to be included in the sample are selected in regular
interval?
a. stratified sampling
b. Systematic sampling
c. cluster sampling
d. simple random sampling
3. What is the sample interval in a study with a population of 200 and a sample size of 35?
a. 5 b. 6 c.7 d. 8
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5. Which of the following illustrates a stratified sampling method?
a. A researcher conducted a survey of 50 randomly selected workers from each of these
categories: high school graduate, with undergraduate degrees, with master’s degree,
and with doctoral degree.
b. A researcher interviewed all freshmen in each of 15 randomly selected public schools in
Zamboanga Sibugay.
c. A researcher doing a research work on students’ reaction of the newly implemented
curriculum and interviewed every 10th student entering the gate.
d. A researcher selected a sample of n = 120 from a population 850 using the Table of
Random Numbers.
9. A population consists of the values (5, 6, 9). How many possible samples of size 2 can be
drawn with replacement from this population?
a. 3 b. 6 c. 9 d. 12
10. What is the mean of the sample in the population consisting the values (3,3,6) and a sample
size of 2?
a. 4 b. 5 c. 6 d. cannot be determined
What’s In
Activity 1: Show me what you’ve got!
Directions: Tell what sampling technique is illustrated in each of the following
situations. Choose your answer from the box below and write your answer on a space
provided.
Simple random sampling Systematics random sampling
__________________2. The names of 50 contestants are written on 50 cards. The cards are
placed in a bag then three names are picked from the bag.
_____________3. Senior high school teachers are interested in knowing what study
techniques their students are utilizing. Rather than assessing all
students, teachers randomly select 10 students from each of the
sections to comprise their sample.
_____________5. A researcher who is studying the effect of social media on office employee
conducted a survey of 50 randomly selected workers from each of
these categories: high school graduate, with undergraduate degrees,
with master’s degree, and with doctoral degree.
What’s New
Activity 2: Can you tell?
Directions: In the given problem below, identify the given value as a Statistic or a
Parameter. Write your answer on the space provided.
______1. A study of every national park’s sale receipts for December shows they bought
in an average of 10 million peso of revenue.
______2. 60 male shoppers of Budget Wise were randomly chosen and their waistlines
were measured revealing an average waistline of 37 inches.
______3. 500 Filipino men were randomly chosen and asked if they are willing to work
abroad leaving their families behind and 65% agreed to work abroad.
______4. After reviewing the arrival times of every flight that landed at the NAIA airport
last month, it was determined that the on-time rate for flights is 68%.
______5. It was found out that all 45 teachers of a certain high school have masters’
degree.
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What is it
1. Simple Random Sampling is one of the simplest forms of collecting data from the
total population. In this method, every element of the population has the same
probability of being selected for inclusion in the sample. One way to do simple
random sampling is using Table of Random Numbers. This contain rows and
columns of mechanically generated digits. Another way of doing this is by using
Lottery Method. Under this, there are two methods;
Example:
A researcher wants to study the effects of social media on 1000 Senior High
School students of Zamboanga Sibugay NHS. He wishes to use the simple random
sampling (without replacement) and to determine how many students should be in
the sample.
Step1: Determine the number of students in the sample. To do this, you can
use the Slovin Formula.
𝑁
𝑛=
1 + 𝑁𝑒 2
Where: n = number of samples needed
N = population size
e = margin of error
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For the margin of error, you can use 5% or 0.05
n = 285.7 or 286
Step2: Assign a number to each of the 1000 Senior High School students.
Step3: Write the numbers on the pieces of papers with the same size and shape
and fold.
Step4: Put all the folded papers in a bowl or box.
Step5: Without looking randomly pick out 286 folded pieces from the bowl. Those
286 randomly picked are samples in the study.
𝑵
𝒌= 𝒏
Where: k = sample interval
N = number of elements in the population (Population size)
n = number of elements in the sample (Sample size)
Example:
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4. Select a number from the whole numbers between 0 and k+1. Since the value of
k is 4, therefore you are going to choose a number between 0 and 5 which are 1, 2,
3, and 4. The chosen value or number is called as the random start.
5. Let’s say you choose number 2, then 2 is your starting number. This means
that the number 2 is your first chosen sample.
6. Then select every 4th student from the sampling frame starting after the 2nd
student.
(Note: See the illustration below to give you an idea on how to use the sample
interval in choosing samples for the study.)
Example:
Suppose you want to know the opinion of 200 students in a certain school
which has a total population of 6,000. If there are 1,200 grades 7; 1,100 grade 8;
1,050 grade 9; 940 grade 10; 900 grade 11 and 810 grade 12 students, how are
you going to choose your sample using stratified sampling?
1. Subdivide the population first into several strata. In this case, we can subdivide
by year level. See the illustration below.
b. Grade 8: ( )( )=
c. grade 9: ( )( )=
Try to compute the rest of the sample size per strata and check your answer on
the table below.
Based on the computed sample size per strata, you can now choose 40 students in
grade 7; 37 in grade 8; 35 in grade 9; 31 in grade 10; 30 in grade 11and 27 in grade 12
for a total of 200 from a population of 6000 students. Take note that, not all elements in
each strata were included in the sample.
Parameter
Statistics
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the population. It usually denoted by a Roman letter. Sample mean ̅ (x bar), sample
standard deviation s and sample variance s2 , are examples of statistic.
Example:
For this survey, each and every one of these 500 students has been asked so we
know the answers from everyone in the entire population; therefore, in this case we have
a Parameter.
In this case, it is impossible to ask all Filipinos. Most probably, only sample of
people who live in the Philippines has been asked and based on their answers, the
researchers made an assumption about the whole population. So what we have is a
Statistic.
Sampling Distribution
To find the mean of the sampling distribution of means ̅ , use the following
formula,
𝐱̅
𝐱̅ =
𝐧
̅ = ̅( ̅)
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Example:
a. All possible sample of size 2 with replacements are listed in the second
column.
b. The corresponding means of all the samples are shown in the third column.
For instance, the first sample drawn is (2,2) and the corresponding mean
( )
̅= = . The second sample consist of (2,3) and the corresponding
( )
mean ̅ = =
Observation Sample ̅
1 (2,2) 2.0
2 (2,3) 2.5
3 (2,5) 3.5
4 (3,2) 3.0
5 (3,3) 4.5
6 (3,5) 4.0
7 (5,2) 3.5
8 (5,3) 4.0
9 (5,5) 5.0
A total of 9 samples with 9 sample means can be drawn from the population.
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Sampling Distribution of Sample Mean 𝒙
̅ with
Replacement and Sample Size n = 2
2.0 1⁄
2.5 1⁄
3.5 1⁄
3.0 1⁄
4.5 1⁄
4.0 1⁄
3.5 1⁄
4.0 1⁄
5.0 1⁄
̅=
d. Compute and ̅ .
1. Mean of population (2,3,5)
+ +
= = = =
̅
̅ = = =
̅ = ( ̅ )( ̅) =( )( ) = =
Notice that the population mean () is equal to the mean of the sampling
distribution of the mean ( ̅ ), that is = ̅ .
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What’s More
1. A certain school has 390 students. Each student studies one of the
following languages; Korean, Japanese, Spanish and Chinese. The table below shows the
number of students who study each of these languages. The researcher wants to look at
the work of the 70 students only.
Population
Language
size
Korean 175
Japanese 96
Spanish 54
Chinese 65
Problem: Find the number of students studying each of these languages that should be
included or part in the sample.
2. A method of simple random sampling that is good for dealing large and dispersed
population and requires more cost and time is _________________.
3. Parameter and statistic are similar yet different measures. Parameter describes
__________________ while Statistic describes _______________.
4. The statistic that is arrived out through repeated sampling from the larger
population is ____________________________.
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What I Can Do
Activity 5: Do me a favor!
Assessment
Directions: Encircle the letter of the correct answer.
3. What type of sampling technique where each list of elements in the population is
used as a sampling frame and the element to be included in the sample are selected
in regular interval?
a. simple random sampling
b. systematic random sampling
c. stratified random sampling
d. cluster random sampling
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4. A researcher conducts an opinion survey in a major city. He randomly picks four
different ethnic groups for a total sample of 300. The researcher then selects 75
participants from each of the four predetermined subgroups? What sampling
method is being utilized?
a. simple random sampling
b. systematic random sampling
c. stratified random sampling
d. cluster random sampling
5. What is the sample interval in a study with a population of 3,500 and a sample size
of 500?
a. 5 b. 6 c.7 d. 8
8. A population consists of the values (5, 6, 9). What is the probability of the sample
mean?
a. b. c. d.
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9. What is the mean of the sample in the population consisting the values
(3, 5,6,9) and a sample size of 2?
a. 5.75 b. 7.67 c.11.5 d. cannot be determined
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Additional Activities
Activity 6: I got you!
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References:
Development Team
Writer: Maribeth R. Saladaga
Sulo National High School
Editor/QA:
Ivy V. Deiparine
Pede I. Casing
Danniel M. Manlang
Illustrator:
Layout Artist:
Management Team:
Evelyn F. Importante
OIC-CID Chief EPS
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