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- 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
- 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.
- 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.
- 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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- 101. Storyset Create your Story with our illustrated concepts. Choose the style you like the most, edit its colors, pick the background and layers you want to show and bring them to life with the animator panel! It will boost your presentation. Check out How it Works. Pana Amico Bro Rafiki Cuate
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- 9. Con 10. Dis
- Poll Survey In gathering reliable data for reasonable decision.
- But not certain with the outcome, but situations may happen.
- Head or Tail is an outcome Sample space- head and tail Example: Dice- the sample space: 1,2,3,4,5,6
- Toss coin
- Number of occurrences=- number of items in each sample points Probability- # of occurrences/ sample points
- 1. not 2. random 3. ra 4. not 5. ra
- 1. not 2. random 3. ra 4. not 5. ra
- Whole number
- Including fractions and decimals
- Including fractions and decimals
- Whole number
- Dis Con Con Con Dis Con dis
- Dis Con dis
- No yes