Basic Statistics PDF

IMMACULATE CONCEPTION ACADEMY, INC. SCIENCE HIGH SCHOOL Basic Statistics Prepared by: Ms. Ros C. Anoran, LPT  STATISTICS A branch of applied mathematics that deals with the collection, organization, presentation, analysis, and interpretation of da...

IMMACULATE CONCEPTION ACADEMY, INC. SCIENCE HIGH SCHOOL Basic Statistics Prepared by: Ms. Ros C. Anoran, LPT  STATISTICS A branch of applied mathematics that deals with the collection, organization, presentation, analysis, and interpretation of data. POPULATION Defined as a group of people, animals, places, things, or ideas.  SAMPLE Subgroup of the population. DESCRIPTIVE STATISTICS Deals with the collection and presentation of data and the summarizing values that describe the group’s characteristics. DESCRIPTIVE STATISTICS Deals with the collection and presentation of data and the summarizing values that describe the group’s characteristics. Example: 1. Measures of central tendency 2. Measures of variation DESCRIPTIVE STATISTICS Example: In a College Algebra examination, 52 out of 60 students were able to receive a passing mark. The average score of the class is 82 out of 100. INFERENTIAL STATISTICS Deals with predictions and inferences based on the analysis and interpretation of the results of the information gathered by the statistician. INFERENTIAL STATISTICS Deals with predictions and inferences based on the analysis and interpretation of the results of the information gathered by the statistician. Example: 1. T-test and Z-test 2. Analysis of variance 3. Chi-square 4. Pearson r INFERENTIAL STATISTICS Example: In a sample survey conducted, 65% of Filipino Generation Z prefer to use twitter while only 34% of Filipino Millenials prefer to use facebook than twitter. VARIABLES OR DATA ITEM Numerical characteristic or attribute associated with the population being studied. VARIABLES OR DATA ITEM Numerical characteristic or attribute associated with the population being studied. Example: 1. Age 2. Sex 3. Income 4. Birthplace CATEGORICAL / QUALITATIVE VARIABLE Classified according to some attributes or categories. Example: Gender, eye color, political references, religion, blood type, civil status, year level, course, profession, and socioeconomic status. NUMERICAL-VALUED / QUALITATIVE VARIABLE Classified according to numerical characteristics. Example: Age in years (5-9, 10-14, 15-19, 20 and above) Height in cm (100-149, 150-199, 200-249) Grade in Math (86-90, 91-95, 96-) NUMERICAL-VALUED / QUALITATIVE VARIABLE A. DISCRETE VARIABLES Variables whose values are obtained by counting. Example: Number of children, number of persons with blue eyes, number of patients with TB, number of males and females NUMERICAL-VALUED / QUALITATIVE VARIABLE B. CONTINUOUS VARIABLES Variables whose values are obtained by measuring. Example: Temperature, distance, area, density, age, height, and weight  TABLE 1.1 Profile of Patients in ABC Hospital Room Job Type of Gender Ages Civil Status Number Description Illness 101 M 25 Engineer Single High Fever 102 F 32 Clerk Typist Married High Fever Typhoid 103 F 38 Housewife Married Fever Bank 104 M 46 Married Cough Manager Widow/Wido 105 M 55 Taxi Driver Pneumonia wer SCALES OF MEASUREMENT In selecting the statistical tool to be used for drawing inferenes on a random sample, the type of measurement scale must be carefully chosen. 1. Nominal Scale 2. Ordinal Scale 3. Interval Scale 4. Ration Scale SCALES OF MEASUREMENT 1. NOMINAL SCALE Classifies elements into two or more categories or classes. The numbers indicate that the elements are different, but the difference is not according to order or magnitude. SCALES OF MEASUREMENT 1. NOMINAL SCALE Example: Gender Types of Electric Consumption M - Male 1 - Residential F - Female 2 - Commercial 3 - Industrial 4 - Government TABLE 1.2 Distribution of XYZ Hospital According to Religion and Gender Religion Male Female Total Roman Catholic 60 75 135 Buddhist 26 30 56 Protestant 3 14 17 Jewish 16 8 24 Total 105 127 232 TABLE 1.3 Distribution of Medical Students of University XXX Grouped According to Race and Civil Status Race Single Married Widow/er Separated Total American 10 5 0 1 16 Chinese 29 8 5 10 52 Japanese 18 11 1 3 33 Filipino 32 3 4 20 59 Total 89 27 10 34 160 SCALES OF MEASUREMENT 2. ORDINAL SCALE Ranks individuals in terms of the degree to which they possess a characteristic. SCALES OF MEASUREMENT 2. ORDINAL SCALE Example: Competition Placement Level of Satisfaction 1 - Champion 1 - Very Satisfied 2 - 1st Runner-up 2 - Satisfied 3 - 2nd Runner-up 3 - Unsatisfied 4 - 3rd Runner-up 4 - Very Satisfied  TABLE 1.4 Anxiety Level of Patients in Hospital YYY Sex 0 1 2 3 Total Male 9 16 2 1 28 Female 21 10 4 7 42 Total 30 26 6 8 70 Legend: 0 = not anxious 1 = low anxiety level 2 = moderate anxiety level 3 = high anxiety level SCALES OF MEASUREMENT 3. INTERVAL SCALE Orders scores from highest to lowest and establishes a uniform unit in the scale so that any distance between two consecutive scores is of equal magnitude. There is also NO ABSOLUTE ZERO in this scale. SCALES OF MEASUREMENT 3. INTERVAL SCALE Example: The aptitude scores from 80 to 90 are of equal difference as that of the aptitude scores from 90 to 100. SCALES OF MEASUREMENT 3. INTERVAL SCALE Example: Temperature 60°C 20°C 10°C -15°C SCALES OF MEASUREMENT 4. RATIO SCALE Orders scores from highest to lowest and establishes a uniform unit in the scale so that any distance between two consecutive scores is of equal magnitude. There is also ABSOLUTE ZERO in this scale. SCALES OF MEASUREMENT 4. RATIO SCALE Example: height, weight, area, volume, speed, rate of doing work. amount of money deposited in a bank SCALES OF MEASUREMENT 4. RATIO SCALE Example: Mass 80 kg 40 kg 10 kg 0 kg