16. In Statistics, it is sometimes impossible
to gather data from the entire population
or collection of objects being examined
in the study but through the use of
samples or representatives of the
population, researchers get a clearer
picture of the whole group being studied.
17. The method of getting samples
is called sampling where it
needs not to be biased to give
justice to the group it represents.
18. Random sampling is a
sampling method of choosing
representatives from the
population wherein every
sample has an equal chance of
being selected.
20. Simple random sampling
the most basic random sampling wherein
elements are usually represented by a number
that are written on equal sized and shaped
papers and then selection of samples is possible
through the lottery method
Drawing number of paper is based from the
desired number of sample.
21. Example:
A researcher writes the name of each
student on a piece of paper, mixes
the papers in a bowl, and draws 7
pieces of paper.
22. Systematic random sampling
a random sampling which uses a list of all
the elements in the population and then
elements are being selected based from the
kth consistent intervals. To get the kth
interval, divide the population size by the
sample size.
24. Stratified random sampling
a random sampling wherein the
population is divided into different strata.
Selection of samples will be
proportionately randomly picked in each
stratum that is why all strata have
representatives in forming the samples.
26. Cluster random sampling
a random sampling wherein population is
divided into clusters and then the clusters
is randomly selected. All elements of the
clusters randomly selected are considered
the samples of the study.
28. Each team will be asked to place papers
with its players’ names into a fishbowl
and randomly drew out five names. The
five names from each team will be
combined to make up the sample. Which
of the following sampling techniques is
being used in this situation?
29. The organizer will create a list of all
players and they will be represented by a
number. Sixty numbers will be picked to
know the samples. Which random
sampling technique did he apply?
30. All players will be grouped according to
their age and will proportionately choose
players to measure their height. Which
random sampling technique did he
apply?
31. Each player of the five teams that will be
randomly chosen to answer the question
prior to the study. Which random
sampling technique did he apply?
33. The Philippine High School has
5,000 senior students. Mr. Manalo,
the principal, wants to obtain
information from the senior high
students as to their plans after
graduation.
34. 1. Principal Manalo writes all the names
of the senior high school students on
small pieces of paper and draws 500
names to participate in the study. Which
random sampling technique does he
apply?
35. 2. The principal creates a list of all
senior high students, decides to survey
every tenth name on the list and later
asks those students that are selected.
Which random sampling technique does
he apply?
36. 3. Mr. Manalo divides the senior high
students as to their grade level and
strand. He proportionately chooses
students from each strand. Which
random sampling technique does he
apply?
37. 4. The principal divides the senior high
school students depending on the
barangay where they live and
randomly picks some of the barangays
to answer the questionnaire. Which
random sampling technique does he
apply?
38. 5. All LRN of each senior high
student are written in pieces of paper
and placed in a bowl. Mr. Manalo
picks the samples based from the table
of numbers. Which random sampling
technique does he apply?
41. 1. You are given a list of all
graduating students in your school.
You decide to survey every tenth
name on the list and ask in which
organization they belong.
42. 2. You wish to make a comparison
about the gender differences on
Mathematics performance. You divide
the population into two groups, male
and female, and randomly pick
respondents from each of the gender.
names.
43. 3. You assign numbers to the
members of the population and
then use draw lots to obtain your
samples.
44. 4. You randomly pick five out of
fifteen barangays to where to
conduct your survey in your
municipality or city.
45. 5. You write the names of
each student in pieces of
paper, shuffles and then
draw eight names.
46. 6. methodical procedure
7. the population is divided into
different strata.
8. population is divided into clusters
9. selection of samples is possible
through the lottery method
10. method of getting samples
48. Most of the researches need numerical values to
easily interpret results of the study. Those values
can be computed based from all the elements of
the population or from the randomly selected
samples that were taken. They can be classified
as to the different measures parameter and
statistic. Parameter and statistic is being
computed through different measures of central
tendency and variability.
49. POPULATION MEAN
The mean is the sum of the data divided by the
number of figures. The mean is used to describe
where the set of data tends to concentrate at a
certain point.
50. To compute for the population mean µ, we
simply add all the data and divide it by number
of data (N).
We apply the formula: µ =
where: µ = the population mean
∑x = the summation of x (sum of the measures)
N = number of elements in the population
51. Below are the grades in
Mathematics of grade 8 students
during the third quarter.
94 85 88 79 78
75 89 91 84 77
53. To compute for the population variance , we
apply the formula:
=
where: x = given data
µ = the population mean
N = number of elements in the population
54. To compute for the population standard
deviation σ, we use the formula:
σ=
where: x = given data
µ = the population mean
N = number of elements in the population
55. Population mean µ, population
variance and population
standard deviation are what we
called parameters.
56. SAMPLE MEAN
The sample mean is the average of all
the data selected from the population.
To compute for the sample mean , we
simply add all the data and divide it
by number of samples (n).
57. We apply the formula:
where: = the sample mean
∑x = the summation of x (sum of
the measures)
n = number of samples
58. Let us now compute for the sample mean,
sample variance and sample standard
deviation.
Assume that the encircled are data that are
randomly selected from the population.
94 85 88 79 78
75 89 91 84 77
60. To compute for the sample variance ,
we apply the formula:
=
where: x = given data
= the sample mean
n = number of samples
61. To compute for the sample standard deviation
(s), we use the formula:
s =
where: x = given data
= the sample mean
n = number of samples
62. The IQ of 10 grade one students are given
below:
Compute for the population mean, population
variance, population standard deviation.
80 128 95 114 82
130 107 100 125 105
63. The scores of the 7 randomly selected
students are given below:
35 15 22
17 31 27 38
Complete the table and compute for the sample mean,
sample variance, sample standard deviation.
65. A sampling distribution of the sample
means is the frequency distribution
table using the computed sample means
from all the possible random samples of
a particular sample size taken from the
given population.
66. PHASES TO MAKE THE
SAMPLING DISTRIBUTION
OF THE SAMPLE MEANS
67. 1. Determine the number of set of all
possible random samples that can be
drawn from the given population by
using the formula NCn where N is the
population size and n is the sample size.
69. 2. List all the possible random samples
and solve for the sample mean of each
set of samples.
70. 3. Construct a frequency distribution
table of the sample means indicating its
number of occurrence or the frequency
and together with its probability.
71. A population consists of the values
(1, 4, 3, 2). Consider samples of size 2
that can be drawn from this population.
72. A.List down all the possible samples and
corresponding sample mean.
76. Coren was able to sell numbers of
pairs of shoes which have sizes of 4,
5, 6, 7, and 8. Consider samples of
size 3 that can be drawn from this
population.
78. The grades show below is the grades in
Statistics and Probability of G11-ABM-Onyx
in the third quarter.
90 85 85 83 82
91 93 75 76 78
80 82 88 91 90
74 83 90 90 84
79. A population consists of the values
(1, 6, 8, 2 and 9). Consider samples of
size 2 that can be drawn from this
population.
Construct the sampling distribution of
the sample means and a histogram.
81. Statisticians do not just describe the variation of
the individual data values about the mean of the
population. They are also interested to know
how the means of the samples of the same size
taken from the same population vary about the
population mean. In this lesson, you will learn
how to describe the sampling distribution of the
sample means by computing its means and
variance.
88. 6. Compute the mean of the
sampling distribution of the
sample means. Follow these steps:
89. a. Multiply the sample mean by
the corresponding probability.
b. Add the results.
90. 7. Compute the variance of the
sampling distribution of the
sample means. Follow these steps:
91. a. Subtract the population mean from each sample
mean.
b. Square the difference.
c. Multiply the results by the corresponding
probability.
d. Add the results.
92. Consider a population consisting of
1, 2, 3, 4, and 5. Suppose samples of
size 2 are drawn from this population.
Describe the sampling distribution of
the sample means.
95. The central limit theorem, which is a
statistical theory, states that when a large
sample size has a finite variance, the
samples will be normally distributed, and
the mean of samples will be
approximately equal to the mean of the
whole population.
96. Illustrative Example: Consider a
population consisting of the values 1, 2, 3,
4, 5, and 6.
A. Compute for the following:
1. population mean,
2. population variance and
3. population standard deviation.
97. 1 2 3 4 5 6
The probability histogram of the population is shown above. Here
n = 1. Since there are 6 possible outcomes and each sample will have
a chance of occurring once, then the probability is 1/6.
.
98. The population mean can also be
obtained using probabilities. Using the
formula:
.
99. How about when you take them two at a time or the sample
size n = 2. It will give us another set of observations. Now,
consider all the possible samples of size 2 that can be drawn with
replacement from the population 1, 2, 3, 4, 5 and 6.
Compute the following:
1.Mean of the sampling distribution of the means
2.Variance of the sampling distribution of the means
3.Standard deviation of the sampling distribution of the means
4.Illustrate the probability histogram of the sampling
distribution of the means.
.
101. This is a graph
It’s a gas giant and
the biggest planet
Jupiter
Mars
Mars is a cold place,
not hot
Venus has a
beautiful name
Venus
Follow the link in the graph to modify its data and then paste the
new one here. For more info, click here
Jupiter Venus Mars
102. This is a graph
Jupiter is the biggest
planet
30% Jupiter
Venus has a
beautiful name
50% Venus
Mars is a cold place,
not hot
20% Mars
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
Jupiter Mars Venus
103. Maybe you need to divide the
content
Venus
Venus has a beautiful
name and is the second
planet from the Sun
Mercury
Mercury is the closest
planet to the Sun and the
smallest one
104. Maybe you need to divide the
content
Venus
Venus has a beautiful
name and it’s hot
Mercury
Mercury is the closest
planet to the Sun
Mars
Despite being red, Mars is
actually a cold place
Jupiter
It’s a gas giant and the
biggest planet
113. This is a graph
It’s a gas giant and
the biggest planet
Jupiter
Mars
Mars is a cold place,
not hot
1,254
8,554
Venus has a
beautiful name
Venus
4,215
Follow the link in the graph to modify its data and then paste the
new one here. For more info, click here
Jupiter
Venus
Mars
114. More graphs
Jupiter is the biggest
planet
35% Jupiter
Venus has a
beautiful name
10% Venus
Mars is a cold place,
not hot
20% Mars
Mercury is the
smallest planet
35%
Mercury
116. Target
60%
40%
Saturn is a gas giant and has rings
Mercury is the closest planet to the Sun
Age
25-38 39-50
Gender Most selled products
● Write the best-selling products
● Write the best-selling products
● Write the best-selling products
● Write the best-selling products
● Write the best-selling products
Annual expenses
Avg. expense: $5000
119. Your can use three columns
Venus
Venus is the second
planet from the Sun.
It’s really hot
Mars
Mars is actually a cold
place. It’s full of iron
oxide dust
Mercury
Mercury is the closest
planet to the Sun and
the smallest one
120. Venus
It’s a planet with very
high temperatures
Mercury
It’s the closest planet
to the Sun
Mars
Mars is actually a very
cold place
You can use six columns
Saturn
It’s composed of
hydrogen and helium
Jupiter
Jupiter is the biggest
planet of them all
Neptune
It’s the farthest planet
from the Sun
121. This is a timeline
Mars is a cold
place, not hot
Jupiter is the
biggest planet
Neptune
Neptune is far
away from Earth
Mercury
Mercury is the
smallest planet
01 02 03 04
Jupiter Mars
122. How the company generates income
Mars
Mars is actually
very cold
Jupiter
Jupiter is the
biggest planet
Neptune
Neptune is far
away from Earth
Saturn
Saturn is a gas
giant with rings
Mercury
Mercury is a small
planet
123. This is a table
Mars Venus Jupiter
Task 1
Task 2
Task 3
Task 4
124. This is a table
Task 1 Task 2 Task 3 Task 4
Descriptio
n
Jupiter is the
biggest planet
Mercury a
small planet
Saturn has
several rings
Neptune is far
away from us
Year 2019 2020 2021 2022
Duration Three months Two weeks Six months Four months
127. Venus
Venus has a beautiful
name
Mars
Mars is actually a cold
place
Mercury
Mercury is the
smallest planet
Jupiter
Jupiter is the biggest
planet
Neptune
Neptune is far away
from Earth
Saturn
Saturn is a gas giant
with several rings
You can use six columns
128. Mercury
Mercury is the
smallest planet
Mars
Despite being red,
Mars is cold
Jupiter
Jupiter is the biggest
planet
Neptune
Neptune is far away
from Earth
Saturn
Saturn is a gas giant
with rings
Competitors
131. This is a map
It’s a gas giant and
the biggest planet
Jupiter
Mars
Mars is a cold place,
not hot
Venus has a
beautiful name
Venus
Mercury
Mercury is the
smallest planet
132. This is a map
Jupiter is the
biggest planet
Jupiter
Venus has a
beautiful name
Venus
Mars is a cold
place, not hot
Mars
Mercury is the
smallest planet
Mercury
133. Venus
Venus has a beautiful
name
Mars
Mars is actually a cold
place
Jupiter
Jupiter is the biggest
planet
Neptune
It’s the farthest planet
from the Sun
You can use four columns
134. Mars
Mars is actually a cold
place
Neptune
Neptune is far away
from Earth
Jupiter
Jupiter is the biggest
planet
01 02 03
You can use three columns
135. This is an infographic
Jupiter
Jupiter is the
biggest planet
Mars
Mars is a cold
place, not hot
Saturn
Saturn is a gas
giant with rings
Venus
Venus has a
beautiful name
01 02
03 04
136. This is an infographic
Mercury
Mercury is the closest planet
to the Sun
Mars
Despite being red, Mars is
actually a cold place
Venus
Venus is the second planet
from the Sun
Idea Produc
t
137. June
Venus has a beautiful
name
January
Mars is actually a cold
place
November
Mercury is the
smallest planet
125K 250K 540K
Monthly data
138. Jupiter
Jupiter is the biggest planet
of them all
Venus
Venus has a beautiful
name and it's very hot
Percentages
Neptune
It’s the farthest planet from
the Sun
Mars
Despite being red, Mars is
actually a cold place
25% 20%
40% 15%
139. Our goals
Venus
Venus has a beautiful
name
Mars
Mars is actually a cold
place
Jupiter
Jupiter is the biggest
planet
Neptune
It’s the farthest
planet from the Sun
140. Jupiter
Jupiter is the biggest
planet
Neptune
It’s the farthest
planet from the Sun
Venus
Venus has a beautiful
name
Our goals
142. Statistics
2019 2020 2021 2022
Avg. spen $15,225 $40,000 $45,000 $65,000
Descriptio
n
Mercury is very
small
Venus has a
nice name
Jupiter is the
biggest planet
Mars is a cold
place, not hot
Customers 12,000 20,000 19,000 40,000
143. Jupiter’s rotation period
The Sun’s mass compared to Earth’s
Distance between Earth and the Moon
9h 55m 23s
333,000
386,000 km
144. 35
4
Mars
78
9
Despite being red, Mars is
actually a cold place
Mercury
Mercury is the smallest planet
of them all
Neptune
Neptune is the farthest planet
from the Sun
91
2
149. ● Write your references here
● Write your references here
● Write your references here
● Write your references here
● Write your references here
● Write your references here
● Write your references here
● Write your references here
List of references
150. ● Write references of internet
● Write references of internet
● Write references of internet
● Write references of internet
● Write references of internet
● Write references of internet
● Write references of internet
● Write references of internet
Research references
● Write references of books
● Write references of books
● Write references of books
● Write references of books
● Write references of books
● Write references of books
● Write references of books
● Write references of books
151. You can replace the image on
the screen with your own
Our team
John Smith
You can replace the image on
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152. Joe Smith
Our team
You can replace the
image on the screen
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178. Add the title here
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2016 2017 2018 2019 2020
“Despite being red,
Mars is actually a
very cold place”
“Mercury is closest
planet to the Sun
and the smallest”
“Neptune is the
farthest-known
planet from the Sun”
“Saturn is a gas
giant and has
several rings”
“Venus has a
beautiful name and
is the second planet”
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179. “Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun and
the smallest”
TITLE 1
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