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2. STATISTICS Chapter 1 Introduction Lesson 1 Chapter 1

3. DATA are defined as factual information used as basis for reasoning, discussion, or calculation, so that meaningful conclusions can be drawn.

4. Definition The word statistics is derived from the Latin word status meaning “state”. Early uses of statistics involved compilation of data and graphs describing various aspects of the state or country. Chapter 1 Introduction Lesson 1

5. Definition Chapter 1 Introduction Lesson 1

6. Statistics as actual numbers (data) The largest earthquake measured 9.2 on the Richter scale. Men are at least 10 times more likely than women to commit murder. One in every 8 South Africans is HIV positive. By the year 2020, there will be 15 people aged 65 and over for every new baby born.

7. Definition Statistics is a science, which deals with the collection , organization, presentation , analysis , and interpretation of quantitative data. Chapter 1 Introduction Lesson 1

8. STATISTICS Statistics the most important science in the whole world; for upon it depends the practical applications of every science and of every art; the one science essential to all political and social administration, all education all organization based on experience, for it only gives results of our experience --Florence Nightingale

9. Uses of Statistics Chapter 1 Introduction Lesson 1

10. The following are some specific uses of statistics: Surveys are design to collect early returns on election day to forecast the outcome of an election. Consumers are samples to provide information for predicting product preference. Chapter 1 Introduction Lesson 1

11. The research physician conducts experiments to determine the effect of various drugs and controlled environmental conditions on humans in order to infer the appropriate method of treatment of a particular disease. Chapter 1 Introduction Lesson 1

12. Branches of Statistics Chapter 1 Introduction Lesson 1

13. Descriptive Statistics It deals with the methods of organizing, summarizing and presenting a mass of data so as to yield meaningful information. Chapter 1 Introduction Lesson 1

14. Example #1 The Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAGASA) measures the daily amount of rainfall in millimeters. They can use descriptive statistics to compute the average daily amount of rainfall every month for the past year. They can use the results to describe the amount of rainfall for the past year.

15. Example #2 Given the daily sales performance for a product for the previous year we can draw a line chart or a column chart (bar) to emphasize the upward/downward movement of the series. Likewise, we can use descriptive statistics to calculate a quantity index per quarter to compare sales by quarter for the previous year.

16. Inferential Statistics It deals with making generalizations about a body of data where only a part of it is examined. This comprises those methods with the analysis of a subset of data leading to predictions or inferences about the entire set of data. Chapter 1 Introduction Lesson 1

17. Sample is part of the population under consideration. Population is the set of all individuals or entities under consideration or study. It may be a finite or infinite collection of objects, events, or individuals, with specified class or characteristics under consideration.

18. Example #1 To examine the performance of the country’s financial system, we can use inferential statistics to arrive at conclusions that apply to the entire economy using the data gathered from a sample of companies or businesses in the country.

19. Example #2 To determine if reforestation is effective, we can take a representative portion of denuded forests and use inferential statistics to draw conclusions about the effect of reforestation on all denuded forests.

20. Example #3 The research division of a certain pharmaceutical company is investigating the effectiveness of a new diet pill in reducing weight on female adults.

21. “It is a capital mistake to theorize before one has data” Sir Arthur Conan Doyle

22. Determine whether the following statements use the area of descriptive statistics or inferential statistics: A bowler wants to find his bowling average for the past 12 games. A manager would like to predict based on previous years’ sales, the sales performance of a company for the next five years. A politician would like to estimate, based on an opinion poll, his chance for winning in the upcoming senatorial election. Chapter 1 Introduction Lesson 1

23. 4. A teacher wishes to determine the percentage of students who passed the examination. 5. A basketball player wants to estimate his chance of winning the most valuable player award based on his current season averages and the averages of his opponents. Determine whether the following statements use the area of descriptive statistics or inferential statistics: Chapter 1 Introduction Lesson 1

24. Definition of Some Statistical Terms Population is the set of all individuals or entities under consideration or study. It may be a finite or infinite collection of objects, events, or individuals, with specified class or characteristics under consideration. Variable is a characteristic of interest measurable on each and every individual in the universe, denoted by any capital letter in the English alphabet. Chapter 1 Introduction Lesson 1

25. Example #1 The PSU Office of Admission is studying the relationship between the score in the college entrance examination during application and the general point average (GPA) upon graduation among graduates of the university from 2010 – 2018. Population: collection of all graduates of the university from 2010 - 2018. Variable of interest: score in the college entrance examination and GPA

26. Example #2 The Department of Health is interested in determining the percentage of children below 12 years old infected by the Hepatitis B/Polio virus in Dagupan City in 2017. Population: set of all children below 12 years old in Dagupan City in 2017. Variable of interest: whether or not the child has ever been infected by the Hepatitis B/Polio virus.

27. Example #3 The research division of a certain pharmaceutical company is investigating the effectiveness of a new diet pill in reducing weight on female adults. Population: set of all female adults who will use the diet pill Variable of interest: Weight before taking the diet pill, weight after taking the diet pill.

28. Types of Variable Qualitative Variable consists of categories or attributes, which have non-numerical characteristics. Examples: year level, sex, religion etc. Quantitative Variable consists of numbers representing counts or measurements Examples: age, height, weight, grades etc. Chapter 1 Introduction Lesson 1 Definition of Some Statistical Terms

29. Classifications of Quantitative Variable Discrete results from either finite or infinite number of countable possible values. Examples: number of students, number of books, etc. b. Continuous results from infinitely many possible values that can be associated with points on a continuous scale. Examples: height, weight, grade point average, etc. Chapter 1 Introduction Lesson 1 Definition of Some Statistical Terms

30. Exercise: Discrete or Continuous? 1. Number of children in a household 2. Number of languages a person speaks 3. Number of people sleeping in stats class 4. Height of children 5. Weight of cars 6. Time to wake up in the morning 7. Speed of the train 8. Age of a person 9. Daily rainfall 10. Time in a race

31. 3. Sample is part of the population under consideration. 4. Parameter is a numerical measurement describing some characteristic of a population. 5. Statistic is a numerical measurement describing some characteristic of a sample. 6. Survey is often conducted to gather opinions or feedbacks about a certain topic. Examples: census survey and sampling survey Chapter 1 Introduction Lesson 1 Definition of Some Statistical Terms

32. MEASUREMENT Measurement is the process of determining the value or label of the variable based on what has been observed.

33. LEVELS OF MEASUREMENT Level 1 Nominal is characterized by data that consist of names, labels, or categories only. Data cannot be arranged in ordering scheme. Examples: Name 4. address Religion 5. sex Civil status 6. degree program Chapter 1 Introduction Lesson 1

34. LEVELS OF MEASUREMENT Level 2 Ordinal involves data that maybe arranged in some order, but differences between data values either cannot be determined or are meaningless. Examples: Military rank 3. year level 2. Job position Chapter 1 Introduction Lesson 1

35. LEVELS OF MEASUREMENT Level 3 Interval is like the ordinal level, with additional property that meaningful amount of differences between data can be determined. There is no absolute zero. Examples: IQ score Temperature Chapter 1 Introduction Lesson 1

36. LEVELS OF MEASUREMENT Level 4 Ratio is the interval level modified to include absolute zero. Examples: Height Width Area Weekly allowance Chapter 1 Introduction Lesson 1

37. Exercise: At what level are the following variables measured Student number Zip codes Final course grades(4.0, 3.00,…) Lengths of TV commercials Blood pressure Gender Family income Academic rank TIN Distances(km) traveled by a bus Chapter 1 Introduction Lesson 1

38. DATA COLLECTION and PRESENTATION Chapter 2 Data Collection and Presentation Lesson 1 Chapter 2

39. Methods of Data Collection In order to have accurate data, the researcher must know the right resources and right way of collecting them.

40. Characteristics of a Good Question A good question is unbiased. Biased Questions Unbiased Questions 1. Do you favor the enrolment procedure employed last semester which makes long lines shorter? 1. Do you favor the enrolment procedure employed last semester? 2. Do you listen to boring classical music? 2. Do you like classical music?

41. 2. A good question must be clear and simply stated. Characteristics of a Good Question Not a good question Good question 1. What is your academic performance last semester? 1. What is your average grade last semester?

42. 3. Questions must be precise. 4. Good questionnaires lend themselves to easy analyses. Characteristics of a Good Question Vague Question Precise Question 1. Do you think male and female are equal? 1. In terms of mathematical ability, do you think male and female are equal?

43. Two Categories of Survey Questions Open question - allows a free response. Example: What do you think can be done to reduce crime? 2. Closed question - allows only a fixed response. Example: Which of the following approaches would be the most effective in reducing crime? Choose one. Get parents to discipline children more. Correct social and economic conditions in slums Improve rehabilitation efforts in jails. Give convicted criminals tougher sentences Reform courts.

44. Types of Data Primary Data -information collected from original source of data. 2. Secondary Data -information collected from published or unpublished sources like books, newspapers and thesis.

45. Methods of Data Collection Direct or Interview Method(Interviewee and Interviewer) Indirect or Questionnaire Method(Written answers) Registration Method(Laws) Observation Method(Senses) Experiment Method (Cause and Effect)

46. Sampling Sampling is the process of selecting units, like people, organizations, or objects from a population of interest.

47. Advantages of Sampling Reduced cost Greater speed Greater scope Greater accuracy

48. Some Definitions Target Population- an entire group a researcher is interested in. Sampled Population-collection of elements from which sample is actually taken. The Frame

49. Probability Sampling Probability sampling method is any method of sampling that utilizes some form of random selection.

50. Probability Sampling Simple Random Sampling -simplest form of random sampling. Examples: table of random numbers, computer generated random numbers, use of calculators 2. Stratified Random Sampling -dividing the population into homogenous subgroups and then taking a simple random sampling

51. Probability Sampling 3. Systematic Random Sampling Systematic sampling with a random start is a method of selecting a sample by taking every unit from an ordered population, the first unit being selected at random. 4. Cluster Random Sampling This sampling method involves dividing the population into clusters (geographical) and then randomly taking samples out of clusters.  

52. Non-probability Sampling Non-probability sampling does not involve random selection of samples. Non-probability samples do not depend upon the rationale of probability theory.

53. Non-probability Sampling Accidental, Haphazard or Convenience Sampling( based primarily on the convenience of the researcher) Purposive Sampling(samples are taken with a purpose in mind)

54. Methods of Data Presentation Methods of Presenting Data Textual Method- a narrative description of the data gathered. Tabular Method- uses rows and columns in describing data. Graphical Method- an illustrative description of data.

55. ORGANIZING DATA

56. Terms Raw Data - information obtained by observing values of a variable. Qualitative data(Qualitative Variable) Quantitative data(Quantitative Variable) Discrete data Continuous data

57. Examples: A study is conducted in which individuals are classified into one of sixteen personality types using Myers-Briggs type indicator. The cardiac output in liters per minute is measured for the participants in a medical study. The number of deaths per 200,000 inhabitants is recorded for several large cities of China caused by NCOV.

58. Frequency Distribution Table(FDT) An FDT is a statistical table showing the frequency or number of observations contained in each of the defined classes or categories.

59. Types of FDT Qualitative or Categorical FDT- a frequency distribution table where the data are grouped according to some qualitative characteristics. Example: Gender of Respondents Number of Respondents Male 38 Female 62 Total 100

60. Example: A sample of rural country arrests gave the following set of offenses with which individuals were charged:

61. Relative Frequency of a Category

62. Percentage

63. BAR GRAPH A bar graph is a graph composed of bars whose heights are the frequencies of the different categories. A bar graph displays graphically the same information concerning qualitative data that a frequency distribution shows in tabular form.

64. PIE CHART A pie chart is also used to graphically display qualitative data. To construct a pie chart, a circle is divided into portions that represent the relative frequencies or percentages belonging to different categories.

65. Types of FDT 2. Quantitative FDT- a frequency distribution table where the data are grouped according to some numerical or quantitative characteristics. Example: Weight(in kilogram) Frequency 7-9 2 10-12 8 13-15 14 16-18 19 19-21 7 Total 50

66. Terms Classes Class limits Class boundaries Class width

67. When forming a frequency distribution, the following general guidelines should be followed: 1)The number of classes should be between 5 and 15. 2) Each data value must belong to one, and only one class. 3) When possible, all classes should be of equal width.

68. Constructing a Quantitative FDT Step 1: Determine the range (R) where: R(Range), HS(Highest Score), LS(Lowest Score) Step 2: Determine the number of classes (k) Where N is the number of observations Step 3: Determine the class size  

69. Constructing a Quantitative FDT Step 4: Enumerate the classes or categories. Step 5: Tally the observations. Step 6: Compute for values in other columns of the FDT as deemed necessary.(True Class Boundaries(TCB), Class Mark(CM), Relative Frequency(RF), Cumulative Frequency(CF), Relative Cumulative Frequency(RCF))

70. Constructing a Qualitative FDT Step 1: Collect the necessary data car bus plane train plane plane car bus train train plane train train train plane train plane plane car bus plane train bus bus bus bus bus bus bus bus Step 2: Tally and make the necessary FDT.

71. Exercise: Construct the FDT of the given data set Age(In years) of 40 Patients Confined at a certain hospital. 5 15 23 27 33 38 44 52 5 15 24 30 33 40 45 53 7 20 25 31 34 42 45 55 10 20 25 31 35 42 50 57 13 21 26 32 36 43 51 57

72. The price for 500 aspirin tablets is determined for each of twenty randomly selected stores as part of a larger consumer study. The prices are as follows:

73. SINGLE-VALUED CLASSES If only a few unique values occur in a set of data, the classes are expressed as a single value rather than an interval of values.

74. Example A quality technician selects 25 bars of soap from the daily production.

75. HISTOGRAMS A histogram is a graph that displays the classes on the horizontal axis and the frequencies of the classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is equal to the frequency of the class.

76. CUMULATIVE FREQUENCY DISTRIBUTIONS A cumulative frequency distribution gives the total number of values that fall below various class boundaries of a frequency distribution.

77. EXAMPLE Table below shows the frequency distribution of the contents in milliliters of a sample of 25 one- liter bottles of soda.

78. OGIVES An ogive is a graph in which a point is plotted above each class boundary at a height equal to the cumulative frequency corresponding to that boundary. Ogives can also be constructed for a cumulative relative frequency distribution as well as a cumulative percentage distribution.

79. STEM-AND-LEAF DISPLAYS In a stem-and-leaf display each value is divided into a stem and a leaf. The leaves for each stem are shown separately. The stem-and-leaf diagram preserves the information on individual observations.

80. The following are the Philippine Achievement Percentile Scores (CAT scores) for 30 seventh- grade students:

81. Exercises Classify the following data as either qualitative data or quantitative data . In addition, classify the quantitative data as discrete or continuous . The number of times that a movement authority is sent to a train from a relay station is recorded for several trains over a two-week period. The movement authority, which is an electronic transmission, is sent repeatedly until a return signal is received from the train. (b) A physician records the follow-up condition of patients with optic neuritis as improved, unchanged, or worse.

82. The following data set gives the yearly food stamp expenditure in thousands of dollars for 25 households in Alcorn County: Construct a frequency distribution consisting of six classes for this data set. Use 0.5 as the lower limit for the first class and use a class width equal to 0.5.

83. Graphical Representations of Data

84. Common Types of Graph 1. Scatter Graph - A graph used to present measurements or values that are thought to be related.

85. Common Types of Graph 2. Line Chart - graphical representation of data especially useful for showing trends over a period of time.

86. Common Types of Graph 3. Pie Chart- a circular graph that is useful in showing how a total quantity is distributed among a group of categories.

87. Common Types of Graph 4. Column and Bar Graph

88. Graphical Presentation of the Frequency Distribution Table 1. Frequency Histogram- a bar graph that displays the classes on horizontal axis and the frequencies of the classes on the vertical axis.

89. Graphical Presentation of the Frequency Distribution Table 2. Relative Frequency Histogram- a graph that displays the classes on the horizontal axis and relative frequencies on the vertical axis.

90. Graphical Presentation of the Frequency Distribution Table 3. Frequency Polygon- a line chart that is constructed by plotting the frequencies at the class marks and connecting the plotted points by means of straight lines.

91. 4. Ogives - graphs of the cumulative frequency distribution. < ogive- the <CF is plotted against the UTCB. > ogive - the >CF is plotted against the LTCB.

92. MEASURES OF CENTRAL TENDENCY Chapter 3

93. Chapter 2 gives several techniques for organizing data. Bar graphs, pie charts, frequency distributions, histograms, and stem-and-leaf plots are techniques for describing data. Often times we are interested in a typical numerical value to help us describe a data set. This typical value is often called an average value or a measure of a central tendency . We are looking for a single number that is in some sense representative of the complete data set

94. EXAMPLE 3.1 The following are examples of measures of central tendency: median priced home, average cost of a new automobile, the average household income in the United States, modal number of televisions per household. Each of these examples is a single number, which is intended to be typical of the characteristics of interest.

95. 113 Measures of Central Tendency A measure of central tendency is a descriptive statistic that describes the average, or typical value of a set of scores There are three common measures of central tendency: the mode the median the mean

96. A data set consisting of the observations for some variable referred to as raw data or ungrouped data . Data is presented in the form of frequency distribution are called grouped data . The measures of central tendency discussed in this chapter will be described for both grouped and ungrouped data since both forms of data occur frequently.

97. Ungrouped Data

98. Mean(   The mean for a sample consisting of n observations is and the mean for a population consisting of N observations is  

99. EXAMPLE: The number of 911 emergency calls classified as domestic disturbance calls in a large metropolitan location were sampled for thirty randomly selected 24 hour periods with the following results. Find the mean number of calls per 24-hour period.

100. EXAMPLE The total number of 911 emergency calls classified as domestic disturbance calls last year in a large metropolitan location was 14,950. Find the mean number of such calls per 24-hour period if last year was not a leap year.  

101. 119 When To Use the Mean You should use the mean when the data are interval or ratio scaled Many people will use the mean with ordinally scaled data too and the data are not skewed The mean is preferred because it is sensitive to every score If you change one score in the data set, the mean will change

102. 120 The Median The median is simply another name for the 50 th percentile It is the score in the middle; half of the scores are larger than the median and half of the scores are smaller than the median

103. Median(   The median of a set of data is a value that divides the bottom 50% of the data from the top 50% of the data. To find the median of a data set, first arrange the data in increasing order . If the number of observations is odd , the median is the number in the middle of the ordered list. If the number of observations is even , the median is the mean of the two values closest to the middle of the ordered list.

104. EXAMPLE To find the median number of domestic disturbance calls per 24-hour period for the data in

105. 123 When To Use the Median The median is often used when the distribution of scores is either positively or negatively skewed The few really large scores (positively skewed) or really small scores (negatively skewed) will not overly influence the median

106. Mode(   The mode is the value in a data set that occurs the most often . If no such value exists, we say that the data set has no mode. If two such values exist, we say the data set is bimodal . If three such values exist, we say the data set is trimodal .

107. 125 The Mode The mode is the score that occurs most frequently in a set of data

108. 126 Bimodal Distributions When a distribution has two “modes,” it is called bimodal

109. 127 Multimodal Distributions If a distribution has more than 2 “modes,” it is called multimodal

110. 128 When To Use the Mode The mode is not a very useful measure of central tendency It is insensitive to large changes in the data set That is, two data sets that are very different from each other can have the same mode

111. 129 When To Use the Mode The mode is primarily used with nominally scaled data It is the only measure of central tendency that is appropriate for nominally scaled data

112. EXAMPLE To find the mode number of domestic disturbance calls per 24-hour period for the data in

113. 131 Relations Between the Measures of Central Tendency In symmetrical distributions, the median and mean are equal For normal distributions, mean = median = mode In positively skewed distributions, the mean is greater than the median In negatively skewed distributions, the mean is smaller than the median

114. Grouped Data

115. Mean , where f-frequency, x-class mark and N-total frequency. , where AM-Assumed mean,  

116. Scores Frequency 9-11 1 12-14 2 15-17 18-20 3 21-23 3 24-26 8 27-29 13 30-32 3 33-35 2 36-38 4 39-41 4 42-44 4 45-47 3 Scores of 50 Students in STATISTICS EXAM

117. Median Where: L=Lower class boundary of the interval where the median lies N=total frequency =cumulative frequency preceding the median class fm =frequency of the median class i =class size  

118. Mode Where: L=exact lower limit of modal class =difference between the frequency of the modal class and the class preceding it =difference between the frequency of the modal class and the class following it i =class size