The document discusses different concepts in statistics and probability including sampling, random variables, probability distributions, and computing probabilities for random variables. It provides examples of discrete and continuous random variables, as well as examples of constructing probability distributions and calculating probabilities corresponding to random variables. The document also briefly covers topics like conditional probability.

1. 1. A method of systematically gathering information on
a fraction of a population (called samples) for the
purpose of inferring quantitative descriptors of the
attributes of the population
Pre-test
a. Survey b. Interview
c. Census d. Experiment

2. 2. A study occurs if the entire population is very small,
or it is reasonable to include the entire population. It is
called a census because data is gathered on every
member of the population.
Pre-test
a. Survey b. Interview
c. Census d. Experiment

3. 3. The purest form of Sampling
Pre-test
a. Simple Random Sampling b. Stratified Sampling
c. Systematic Sampling d. Cluster Sampling

4. 4. What is the sampling technique used when the
population is large or when it involves subjects
residing in a large geographic area?
Pre-test
a. Simple Random Sampling b. Stratified Sampling
c. Systematic Sampling d. Cluster Sampling

5. 5. What is the sampling method that relies on
arranging the target population according to some
ordering scheme and involves a random start and
then proceeds with the selection of every kth element
from then onwards?
Pre-test
a. Simple Random Sampling b. Stratified Sampling
c. Systematic Sampling d. Cluster Sampling

6. 6. What is the population mean of
X={15,25,35,45,55}
Pre-test
a. 35 b. 30
c. 40 d. 25

7. 7. Which of the following is a discrete random
variable?
Pre-test
a. Length of wire ropes
b. Number of soldiers in the troop
c. Amount of paint used in repainting the building
d. Voltage of car batteries

8. 8. How many ways are there in tossing two coins
once?
Pre-test
a. 4
b. 3
c. 2
d. 1

9. Classify the following random variables as discrete or
continuous.
Pre-test
9. The weight of the professional wrestlers
10. The number of winners in lotto for each day

10. Statistics and
Probability

12. In decision making, we use statistics although some of us
may not be aware of it. An inquiry could be answered or a problem
could be solved through the use of statistics. In fact, without
knowing it we use statistics in our daily activities.

13. ● Mathematics
● Economics
● Research
● Practicalities of Life
Statistics

15. ● Win or Lose
● Picked
● Chances – Probabilities of an event
● Random Outcomes - uncertain
Probability

18. ● Outcome- result of an experiment.
● Sample Space- result of all outcomes
in an experiment

19. ● In a coin toss,
what is the
probability of
getting a head?
● ½
Probability

20. ● In rolling a die,
what is the
probability of
getting a number
less than 5?
● 2/3
● 4,3,2 or 1 = 4/6
Probability

21. ● What is the probability
of rolling, on a fair
dice:
● a. a 3?
● b. an even number?
● c. zero?
Probability

22. ● Answer:
● a. P(‘3’) = 1/6 ;
● b. P(Even)= 3/6 = 1/2
;
● c. P(‘0’) = 0 ;
Probability

23. ● What is the
probability of
getting a 2 from a
deck of card?
● 1/13
● 52 cards, 4 cards
with 2 = 4/52
Probability

24. ● What would be the
probability of
● a. picking a black card at
random from a standard
deck of 52 cards?
● b. picking a face card (i.e.
a king, queen, or jack)?
Probability

25. ● Answer:
● a. P(Black) = 26/52= ½ ;
● b. P(Face)= 12/52 = 3/13
Probability

26. Random Variables

27. Definitions of Random Variable
• A random variable is a result of chance event, that you can
measure or count.
• A random variable is a numerical quantity that is assigned to
the outcome of an experiment. It is a variable that assumes
numerical values associated with the events of an experiment.
• A random variable is a quantitative variable which values
depends on change.
• NOTE: We use capital letters to represent a random variable.

28. Example 1
Suppose two coins are tossed and we are
interested to determine the number of tails
that will come out. Let us use T to represent
the number of tails that will come out.
Determine the values of the random variable
T.

29. Example 1

30. Number of
Tails
0 1 2
Sample
Points
HH HT
TH
TT
Number of
Occurrences 1 2 1
Probability 1/4 2/4= 1/2 1/4

31. 1.The gender of the people who enter a
library.
2.The number of books a person have.
3. The number of tellers busy at 1 pm.
4.The method the customer use to pay.
5.The number of costumers who pay by
cash.

32. Suppose there are 2 people to be tested
in Covid-19. Let X be the random variable
representing the number of infected that
occur. Find the values of the random
variable X.

33. Types of Random
Variable

34. Types of Random Variable
Continuous Discrete
A discrete random
variable has a
countable number of
possible values.
A continuous random
variable can assume
an infinite number of
values in one or more
intervals

35. Discrete Random Variable
• Finite number of distinct values
• Finite- countable
• Distinct- different values

36. Discrete Random Variable
• The values are exact and can be
represented by nonnegative whole
numbers.

37. Discrete Random Variable
• Categorical variables can be considered discrete
variables. Example: whether a person has
normal BMI or not, you can assign one (1) as the
value for normal BMI and zero (0) for not normal
BMI. You can also put numbers to represent
certain categorical variables with more than two
categories. You can also use ordinal variables,
like how much they like adobo on a scale of 1 to
10 (where 1 means favorable and 10
unfavorable)

38. Discrete Random Variable
Examples
• Number of pens in a box
• Number of ripe bananas in a basket
• Number of COVID-19 positive cases in
Buayan

39. Continuous Random Variable
• Takes any value within a range.
• are random variables that take an
infinitely uncountable number of
possible values, typically
measurable quantities.

40. Continuous Random Variable
• Values are represented not only by
nonnegative whole numbers but
also fractions and decimals and
are often results of measurement.

41. Continuous Random Variable
Examples
• Length of electric wires
• Voltage of car batteries
• Amount of sugar in a cup of coffee

42. Quiz

43. Two balls are drawn in succession without
replacement from box containing 5 red balls and
6 blue balls. Let Z be the random variable
representing the number of blue balls. Find the
values of the random variable Z.

44. • Let B represent the blue ball and R represent
the red ball.
Sample Space = {RR, RB, BR, BB}
Possible Outcomes Value of the random
variable Z
RR 0
RB 1
BR 1
BB 2
Z= {0,1,2}

45. c.) Scores of a student in a 10- item test.
Z= {0,1,2,3,4,5,6,7,8,9,10}
d.) Product of two numbers taken from two boxes
containing numbers 0 to 5.
Write all possible values of each random variable:

46. Z= {0,1,2,3,4,5,6,8,9, 10, 12, 15, 16, 20, 25}

47. Classify each random variable as discrete or
continuous.
1.Score of a students in a quiz.
2.How long students ate breakfast.
3.Time to finish running 100 m.
4.Amount of paint utilized in a building project.
5.The number of deaths per year attributed to
lung cancer.
6.The speed of a car.
7.The number of dropout in a school district for a
period of 10 years.

48. Classify each random variable as discrete or
continuous.
8. The number of voters favoring a candidate.
9. The time needed to finish the test.
10.Number of eggs a hen lays.

49. Probability
Distribution of
Discrete Random
Variables

50. A discrete probability distribution consists of the values a random
variable can assume and the corresponding probability
Example:
If two coins are tossed, the possible outcomes are HH, HT, TH, TT.
If X is the random variable of head,
Discrete Probability Distribution
Possible
Outcomes
Value of the
random
variable X
HH 2
HT 1
TH 1
TT 0
No Heads
1
4
One Head
2
4
=
1
2
Two Heads
1
4
Number of
heads, X
0 1 2
Probability,
P(X)
¼ ½ ¼

51. Example 1: Construct a
probability distribution for
rolling a single die.
Sample space= {1, 2, 3, 4, 5, 6}
Each out come has a probability of 1/6.
Outcome, X 1 2 3 4 5 6
Probability, P(X) 1/6 1/6 1/6 1/6 1/6 1/6

52. Properties of Discrete Probability
Distribution
1.The sum of all probabilities should be 1.
P(X)= 1
Number
of heads,
X
0 1 2
Probability
, P(X)
¼ ½ ¼
P(X)= ¼ + ½ + ¼ = 1

53. Properties of Discrete Probability
Distribution
2. Probabilities should be confined between
zero (0) and 1.
0 ≤ P(X) ≤ 1
Number
of heads,
X
0 1 2
Probability
, P(X)
¼ ½ ¼

54. Example 2: Determine whether the
distributions is a discrete probability
distribution
0 ≤ P(X) ≤ 1
P(X)= 1

55. Example 3: Suppose three coins are tossed. Let Y be the
random variable representing the number of tails. Construct
the probability distribution and draw the histogram

56. Example 4: Box A and Box B contain 1,2,3,4. Write the
probability mass function and draw the histogram of the
sum when one number from each box is take at a time, with
replacement.

57. Example 4: Box A and Box B contain 1,2,3,4. Write the
probability mass function and draw the histogram of the
sum when one number from each box is take at a time, with
replacement.

58. Computing
Probability
Corresponding to a
given random
variable

60. Example 1: The following data show the probabilities for the
number of cars sold in a given day at a car dealer store.
a.Find P (X ≤ 2)
𝑃 𝑋 ≤ 2 = 𝑃(0) + 𝑃(1) + 𝑃(2)
= 0.100 + 0.150 + 0.250
𝑃 𝑋 ≤ 2 = 0.500
b.Find 𝑃(𝑋 ≥ 7)
𝑃 𝑋 ≥ 7 = 𝑃 7 + 𝑃 8 + 𝑃 9 + 𝑃(10)
= 0.050 + 0.040 + 0.025 + 0.015
𝑃 𝑋 ≥ 7 = 0.130

61. Example 1: The following data show the probabilities for the
number of cars sold in a given day at a car dealer store.
c. Find P (1 ≤ 𝑋 ≤ 5)
𝑃 (1 ≤ 𝑋 ≤ 5) = 𝑃 1 + 𝑃 2 + 𝑃 3 + 𝑃 4 + 𝑃(5)
= 0.150 + 0.250 + 0.140 + 0.090 + 0.080
𝑃 (1 ≤ 𝑋 ≤ 5)𝑃 𝑋 ≤ 2 = 0.710

62. Example 2: In a convenient store, the number of tellers (X) busy with
costumers at 12:00 noon varies from day to day. Past records indicate
that the probability distribution of X as follows
1. What is the probability that exactly
four tellers are busy at 12:00 noon?
P(X=4)= 0.212
2. What is the probability that at least,
two tellers are busy at 12:00 noon?
P(X ≥ 2) = P(2)+ P(3)+ P(4)+ P(5)+ P(6)
= 0.078+0.155+0.212+0.262+0.215
= 0.922

63. Example 2: In a convenient store, the number of tellers (X) busy with
costumers at 12:00 noon varies from day to day. Past records indicate
that the probability distribution of X as follows
3. What is the probability that fewer than
five tellers are busy at 12:00 noon?
P (X<5)= P(0)+P(1)+P(2)+P(3)+(4)
= 0.029+0.049+0.078+0.155+0.212
=0.523

64. Example 2: In a convenient store, the number of tellers (X) busy with
costumers at 12:00 noon varies from day to day. Past records indicate
that the probability distribution of X as follows
1. What is the probability that exactly
four tellers are busy at 12:00 noon?
2. What is the probability that at least,
two tellers are busy at 12:00 noon?
3. What is the probability that fewer than
five tellers are busy at 12:00 noon?

65. “This is a quote, words full of wisdom that
someone important said and can make
the reader get inspired.”
—SOMEONE FAMOUS

66. SOCIOLOGY AND MATHS
Here you can give a brief description of the topic you
want to talk about. For example, if you want to talk
about Mercury, you can say that it’s the smallest planet
in the entire Solar System

67. SOCIOLOGY
You can enter a subtitle here if you need it

68. POPULATION
Venus has a
beautiful name
CHINA
These are the regions with the highest population
It is the biggest
planet of them all
BRAZIL
It’s the farthest
planet from the Sun
INDIA

69. HISTORY OF SOCIOLOGY
Mercury is the closest
planet to the Sun
MERCURY
Venus is the second
planet from the Sun
VENUS
It’s the biggest planet in
the Solar System
JUPITER
Saturn is a gas giant
and has several rings
SATURN
Neptune is the farthest
planet from the Sun
NEPTUNE
Despite being red, Mars
is actually a cold place
MARS

70. MERCURY
Venus has a beautiful
name and is the second
planet from the Sun
HOW TO USE MATHS IN SOCIOLOGY
VENUS
It is the closest planet to
the Sun and the smallest
one in the Solar System

71. PROBABILITY
You can enter a subtitle here if you need it

72. APPLICATIONS OF PROBABILITY
It’s the closest planet to the
Sun and the smallest in the
Solar System
MERCURY
Venus has a beautiful name
and is the second planet
from the Sun
VENUS
Despite being red, Mars is
actually a cold place. It’s full
of iron oxide dust
MARS

73. VENN DIAGRAMS
50% 30%
20%
It’s the closest planet to the Sun and
the smallest in the Solar System
MERCURY
Venus has a beautiful name and is
the second planet from the Sun
VENUS
Despite being red, Mars is actually a
cold place. It’s full of iron oxide dust
MARS

74. A PICTURE
ALWAYS
REINFORCES
THE CONCEPT
Images reveal large amounts of
data, so remember: use an image
instead of a long text. Your audience
will appreciate it

75. P(A｜B) = P(A∩B) ⁄ P(B)
CONDITIONAL PROBABILITY
Saturn is a gas giant and
has several rings
SATURN
Neptune is the farthest
planet from the Sun
NEPTUNE
Pluto is now considered a
dwarf planet
PLUTO
Earth is the third planet
from the Sun
EARTH

76. AWESOME

77. PROBABILITY
FACE A
Mars is a cold place. It's
full of iron oxide dust,
which gives the planet
its reddish cast
First Move 50%
Second Move 25%
FACE B
Venus has a nice name
and is the second planet
from the Sun. It’s terribly
hot
Third Move 23%
Fourth Move 50%

78. Big numbers catch your audience’s attention

79. Mars is actually a cold place
Neptune is the farthest planet

80. EXERCISE 1
Answer the following questions
A bag contains 4 red rings, 8 green rings and 11 white rings. If a ring is drawn from
the bag at random, what is the probability that this ring is white?
What is the probability of throwing two dice and getting the sum of the fallen
numbers greater than 3?
A die is rolled and a coin is tossed, find the probability that the die shows an odd
number and the coin shows a head
Someone at the post office placed three letters randomly into three envelopes.
What is the probability that at least one of the recipients gets his letter?

81. STATISTICS
You can enter a subtitle here if you need it

82. STATISTICS
Mercury is the closest
planet to the Sun and
the smallest one
MERCURY
Venus has a beautiful
name and is the second
planet from the Sun
VENUS
Despite being red, Mars
is a cold place. It's full of
iron oxide dust
MARS
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here
It’s the farthest planet
from the Sun
38%
33%
29%

83. VENUS SATURN TOTAL
MERCURY 21 39 60
MARS 135 45 180
TOTAL 156 84 240
MAKING TWO WAY TABLES
Venus has a beautiful name and is the second planet from the Sun
Column totals
Row
totals

84. SCATTER PLOTS
Venus has a beautiful
name and is the second
planet from the Sun
VENUS
Despite being red, Mars
is a cold place. It's full of
iron oxide dust
MARS
Follow the link in the graph to modify its data and then paste the new one here. For more info, click here

85. DESCRIBING DATA
VARIABLE
Categorical
Numeric
Continuous Discrete Original Nominal

86. HOW TO TESTING AN HYPOTHESIS
Venus is the
second planet from
the Sun
VENUS
Saturn is a gas
giant and has
several rings
SATURN
Mercury is the
closest planet to
the Sun
MERCURY
Despite being red,
Mars is actually a
cold place
MARS

87. CHECKLIST
MARS
Mars is a cold place
It’s the fourth planet
It has a thin atmosphere
It’s a red planet
VENUS
Venus has a beautiful name
It’s the second planet
Venus is a terrestrial planet
Its atmosphere is poisonous
It's full of iron oxide dust It's full of iron oxide dust

88. HYPOTHESIS TESTING
REJECTION ACCEPT REJECTION
Jupiter is the biggest
planet of them all
REJECTION
Venus is the second
planet from the Sun
ACCEPT

89. EXERCISE 2
The twins John and Jenna have created a table of their school grades, which
they got throughout the whole semester in certain subjects
MUSIC SPANISH BIOLOGY PHYSICS
JOHN 1,2,3,5,5,2 3,3,3,1,1,2 1,1,1,3,4,1 2,2,3,1,5,4
JENNA 4,4,1,2,2 2,2,2,2 5,5,4,4,3,4,3,3 1,1,2,1,2,2,2
Calculate the final grade of the twins in all subjects, if the range of the school grades
is from 1 to 5

90. A PICTURE IS
WORTH A
THOUSAND
WORDS

91. You can replace the image on
the screen with your own work.
Just delete this one, add yours
and center it properly
DESKTOP WEB

92. You can replace the image on
the screen with your own work.
Just delete this one, add yours
and center it properly
TABLET APP

93. You can replace the image on
the screen with your own work.
Just delete this one, add yours
and center it properly
MOBILE APP

94. OUR TEAM
You can replace the
image on the screen
with your own
JENNA DOE
You can replace the
image on the screen
with your own
TOM JIMMY
You can replace the
image on the screen
with your own
SARAH DOE

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