Nature of Statistics Nature of Statistics Nature of Statistics
- 2. Objectives At the end of the lesson, the students are expected to: • define statistics; • identify questions that could be answered using a statistical process and describe the activities involved in a statistical process; • summarize the different classification of variables and data, • identify appropriate sampling techniques in the selection of participants in the study and; • evaluate expression with summation notation.
- 3. Statistical Analysis is the process of collecting and analyzing large volumes of data in order to identify trends and develop valuable insights.
- 4. What is Statistics? Statistics is defined as a science that examines and investigates ways to process and analyze the data gathered. It provides procedure in data collection, presentation, organization, and interpretation to have meaningful idea that is useful to decision-makers.
- 5. NATURE OF STATISTICS General Uses of Statistics 1. Statistics aids in decision making a. Provides comparison b. Explains action that has taken place c. Justifies a claim or assertion d. Predicts future outcome e. Estimates unknown quantities 2. Statistics summarizes data for public use
- 6. Purpose of Statistics Task of Statistics “to reduce large masses of data to some meaningful values” Descriptive Statistics “to tell something about a particular group of observation” Inferential Statistics “there is an intent of predicting what the large population is like out of the sample size“
- 7. Division of Statistics Descriptive Inferential The totality of methods and treatments employed in the collection, description, and analysis of numerical data. To tell something about a particular group of observation. The logical process from sample analysis to a generalization of conclusion. Also Statistical Inference or Inductive Statistics
- 8. Descriptive Statistics • methods concerned with the collection, description, and analysis of a set of data without drawing conclusions or inferences about a larger set. • the main concern is simply to describe the set of data such that otherwise obscure information in brought out clearly • Conclusions apply only to the data on hand
- 9. Examples • Life expectancy: In 2022, the life expectancy at birth in the Philippines was 69.27 years. • temperature of her patient for the last 24 hours. • Funding allocation: In a study of the Department of Health-Medical, the clinical departments with the highest funding allocation were Medicine (29.68%), Surgery (26.25%), and Neurosciences (15.99%).
- 10. Inferential Statistics • methods concerned with making predictions or inferences about a larger set of data using only the information gathered from a subset of this larger set. • the main concern is not merely to describe but actually predict and make inferences based on the information gathered. • conclusions are applicable to a larger set of data which the data on hand is only a subset
- 11. Example • Estimating the mean marks of students in a country. If the mean marks of 100 students in a country are known, inferential statistics can be used to approximate the mean marks of all students in the country. • A doctor wants to prescribe medication to her patient based on the average temperature for the last 24 hours. • Determining if a teaching method is effective. A t-test can be used to compare the exam scores of two math classes taught by different teachers. If there is a statistically significant difference in scores, it may be inferred that one teacher's method is more effective.
- 12. Statistical Process There are basically 5 steps in conducting a statistical investigation. These are: • Defining the problem • Collecting and organizing relevant information • Presenting the data • Analyzing the data • Interpreting the results
- 13. Population vs Sample Population Sample Consist of all the members of the group about which to draw conclusion. Portion or part, of the population of interest selected for analysis. A E H L K I D C G J F B P M O N S R Q P W V U T Z Y X population sample
- 14. Parameter and Statistic Parameter Statistic Numerical index describing a characteristic of a population. Numerical index describing a characteristic of a sample.
- 15. Sources of Data Primary Data Secondary Data Data that come from original source. Data that are taken from previously recorded data. Examples: Interview Mail-in questionnaire Survey Experimentation Examples: Information in research Business periodicals Financial statements Government reports
- 16. Constant and Variable Constant Variable Characteristics of objects, people, or events that does not vary. Characteristics of objects, people, or events that can take of different values. Example: Boiling temperature in °C Example: Weight
- 17. A variable • is a characteristic or attribute of persons or objects which can assume different values or labels for different persons or objects under consideration. • A piece of information recorded for every item or experimental unit. Variable & Types of Data
- 18. Types of Variables Variable Qualitative (Categorical) Quantitative (numerical) Discrete Continuous
- 19. • are variable that takes on numerical values representing an amount or quantity. • The data collected about a quantitative variable is called quantitative data. • Age, height, test scores, weight, prices of cars, number of cars owned, annual income, market sales and stock prices are examples of quantitative variables that can be classified as either discrete or continuous. QUANTITATIVE VARIABLE
- 20. Discrete variable – a variable which can assume finite, or, at most, countably infinite number of values; usually measure by counting or enumeration. Some measures of behavior of subjects and expected to be influenced by the independent variable.
- 21. Examples of discrete variables are: 1. the number of days in a week, 2. the number of children in the family, 3. the number of students in the classroom, 4. the number of teachers in school, 5. the number of house and lots sold on a particular day, 6. the number of people visiting a bank, 7. the number of cars in a parking lot, 8. the number of poultry owned by a farmer, 9. the number of employees of a company.
- 22. Continuous variable a variable which can assume any of an infinite number of values and can be associated with points on a continuous line interval. The possible values of the variable belong to a continuous series. Between any two values of the variable, an indefinitely large number of in-between values may occur.
- 23. Examples of continuous variables are values obtained by measurement such as weight, height, volume, temperature, distance, area, density, age and price of commodity.
- 24. Qualitative Variable – a variable that yields categorical responses. a. Dichotomous qualitative variable can be made only in two categories: yes or no, defective or non-defective, etc. b. Multinomial qualitative variable can be made into more than two categories such as educational attainment, nationality, religion. QUALITATIVE OR CATEGORICAL VARIABLE
- 25. Classification of Variables Experimental Classification Mathematical Classification
- 26. Experimental Classification Independent Variables Dependent Variables Controlled by experimenter/ researcher, and expected to have Some measures of behavior of subjects and expected to be influenced by the independent variable
- 27. Mathematical Classification It can assume any of an infinite number of values and can be associated with points on a continuous line interval. Continuous Variables Discrete Variables Example: Height, weight, volume
- 28. is the process of determining the value or label of a particular variable for a particular experimental unit. An experimental unit is the individual or object on which a variable is measured. Measurement
- 29. Levels of Measurement Scale Legitimate Statistics Nominal •Indicates a difference Ordinal •Indicates a difference •Indicates a direction of the difference (e.g., more than or less than) Interval •Indicates a difference •Indicates a direction of the difference •Indicates the amount of difference (in equal intervals) Ratio •Indicates a difference •Indicates a direction of the difference •Indicates the amount of difference •Indicates an absolute zero
- 30. Qualitative Variable Categories Gender Automobile Ownership Type of Life Insurance Owned Male, Female Yes, No Term, Endowment, Straight-Life, Others, None Property of a set of categories such that an individual or object is included in only one category. Mutually Exclusive Property of a set of categories such that each individual or object must appear in only one category. Exhaustive Example Nominal Level
- 31. Ordinal Level Example Qualitative Variable Categories Student class designation Product satisfaction Movie classification Faculty Rank Hotel Ratings Student Grades Freshman, Sophomore, Junior, Senior Unsatisfied, Neutral, Satisfied, Very Satisfied G, PG, PG-13, R-18, X Professor, Associate Prof., Assistant Prof, Instructor , , , , 1.0, 1.25, 1.50, 1.75, 2.00, …
- 32. Example Qualitative Variable Temperature (in degree oC or oF) Calendar Time (Gregorian, Hebrew, or Islamic) Interval Level
- 33. Example Qualitative Variable Weight ( in pounds or kilograms) Age (in years or days) Salary (in Philippine peso) Ratio Level
- 34. Classification of Data Data Qualitative Nominal Ordinal Quantitative Interval Ratio
- 35. CLASSIFICATION OF STATISTICAL PROCEDURES • PARAMETRIC STATISTICS are based on the assumptions about the distribution of the population from which the sample was taken. It can be said that the data are interval and its distribution is normal. • NONPARAMETRIC STATISTICS are not based on assumptions, that is, the data can be collected from a sample that does not follow a specific distribution.
- 36. It is the policy of the State to protect the fundamental human right of privacy, of communication while ensuring free flow of information to promote innovation and growth. The State recognizes the vital role of information and communications technology in nation-building and its inherent obligation to ensure that personal information in information and communications systems in the government and in the private sector are secured and protected. Republic Act No 10173 Data Privacy Act of 2012
- 37. Philippines Population • 116,518,032 as of 5:56 PM March 19, 2025 • 109,033,245 01 May 2020
- 39. Determining the Sample Size Slovin’s Formula 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑖𝑧𝑒, 𝑛 = 𝑁 1 + 𝑁𝑒2 Where: n = sample size N = population size e = margin of error
- 40. Sampling Techniques Random Sampling Non-Random Sampling Simple Random Systematic Stratified Multiple Stage Convenience Purposive Quota Snowball Cluster
- 41. Simple Random Sampling/Lottery A E H L K I D C G J F B P M O N S R Q W V U T Z Y X D J O X G B Population Sample
- 42. Systematic Sampling A E H L K I D C G J F B P M O N S R Q W V U T Z Y X C W H M R Population Sample
- 43. Stratified Sampling A E H L K I C G J F B P M O N S R Q T D B D (25%) (50%) (25%) S P (25%) (25%) O I M F (50%) Sample Population
- 44. Cluster Sampling A E H L K I D C G J F B P M O N S R Q U T Population Sample A B N O M C U T S
- 45. Multi-Stage Sampling A E H L K I D C G J F B P M O N S R Q U T Population Sample A B N O M C U T S Sample of Cluster A S N
- 48. Quota Sampling A E H L K I C G J F B P M O N S R Q T D B D (25%) (50%) (25%) T S (37.5%) (37.5%) I M (25%) Sample Population = 20 A P
- 50. Methods in Collecting Data Direct or Interview Method Indirect or Questionnaire Method Registration Method Observation Method Experiment Method
- 51. Methods in Presenting Data Textual Method Tabular Method Graphical Method data is presented in paragraph form. data is presented in rows and columns. data is presented in visual form.
- 52. Textual Form Table 1 presents the frequency and percentage distribution of the respondents according to gender. The table shows that majority of the respondents are female with 3,625 or 72.5%, while 1,375 or 27.5% are male. Most of the Nursing students are female, it only shows that Nursing is a course more favorable for female.
- 53. Example: Tabular Form Gender Frequency Percentage Male 1,375 27.5 Female 3,625 72.5 Total 5000 100 Table 1 Frequency and Percentage Distribution of the Nursing Students According to Gender
- 55. = + + + + = n 1 i n 3 2 1 i X ... X X X X = 4 1 i 3 i X = + 3 1 i i ) 2 X ( = + 2 1 i 3 i i ) Y X ( = n 1 i i X is used to denote the sum of all the Xi’s from i = 1 to i = n; by definition, The symbol Write the following expressions in expanded form: Summation Notation
- 56. Summation Properties • The Summation of a Constant. σ𝒌=𝟏 𝒏 𝒄 = 𝒏𝒄 • The Summation of a Sum σ𝒊=𝟏 𝒏 𝒙𝒊 + 𝒚𝒊 = σ𝒊=𝟏 𝒏 𝒙𝒊 + σ𝒊=𝟏 𝒏 𝒚𝒊
- 57. = 4 1 i i iY X 2 Evaluate the following notations using the values below: X1 = 1 Y1 = 0 Z1 = 4 X2 = 3 Y2 = 8 Z2 = 7 X3 = 2 Y3 = 1 Z3 = -2 X4 = 5 Y4 = 6 Z4 = 3 = − 4 1 i i i i ) X Y ( Z = + 3 1 i 2 i i ) Z X ( Summation Notation