Introduction to Statistics PDF - La Salle College Antipolo

Introduction to Statistics La Salle College Antipolo Learning Targets Define statistics Continuous and Discrete Differentiate types of Variables statistics. Identify four levels of Define the basic terms in measurement...

Introduction to Statistics La Salle College Antipolo Learning Targets Define statistics Continuous and Discrete Differentiate types of Variables statistics. Identify four levels of Define the basic terms in measurement statistics Give examples for each level Population and Sample of measurement Parameters and Statistic Differentiate four levels of Data and Variable measurement Qualitative and Quantitative Variables Statistics Is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data. ✓ Descriptive Statistics ✓ Inferential Statistics Population A complete collection, or set, of individuals or objects or events whose properties are to be analyzed. Consist of all subject that are being studied. Sample A sub collection of members selected from a population is a group of subject selected from a population Population VS. Sample Population VS. Sample Give examples of population and sample Let’s Try 1: Identify the population and sample A survey of 1353 Filipino households found that 18% of the households own a computer. A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was 125,000. Parameter ▸ A numerical value summarizing all the data of an entire population. Statistic ▸ A numerical value summarizing the sample data Parameter VS. Statistic Parameters Statistics Population Sample Mean Mean (µ) (x bar) Population Sample Variance (𝝈𝟐 ) Variance (𝒔𝟐 ) Population Sample Standard Standard Deviation (𝝈) Deviation (𝒔) Statistics Is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data. ✓ Descriptive Statistics ✓ Inferential Statistics Descriptive Statistics Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive Statistics Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Inferential Statistics Inferential statistics are tools that statisticians use to draw conclusions about the characteristics of a population, drawn from the characteristics of a sample, and to determine how certain they can be of the reliability of those conclusions. Inferential Statistics Inferential statistics are used to make generalizations about large groups, such as estimating average demand for a product by surveying a sample of consumers' buying habits or attempting to predict future events. Descriptive vs. Inferential Descriptive A bowler wants to find his bowling average for the past 12 months Inferential A bowler wants to estimate his chance of winning a game based on his current season averages and the average of his opponents Descriptive vs. Inferential Descriptive A housewife wants to determine the average weekly amount she spent on groceries in the past 3 months Inferential A housewife would like to predict based on last year’s grocery bills, the average weekly amount she will spend on groceries for this year. Descriptive vs. Inferential Descriptive A politician wants to know the exact number of votes he receives in the last election. Inferential A politician would like to estimate based on opinion polls, his chance for winning in the upcoming election. Let’s Try 2: Descriptive or Inferential A recent study examined the math and verbal SAT scores of high school seniors across the country. Which of the following statements are descriptive in nature and which are inferential. 1. The mean math SAT score was 492. 2. 80% of all students taking the exam will continue for college. 3. 32% of the students scored above 610 on the verbal SAT. 4. The mean verbal SAT score was 475. 5. The math SAT scores are higher than they were 10 years ago. Data The value of the variable (such as measurements, genders, survey responses) associated with one element of a population or sample. This value may be a number or a word. Variable Is any characteristics, number, or quantity that can be measured or counted about each individual element of a population or sample Variable Is a characteristic or attribute that can assume different values ✓ Age ✓ Gender ✓ Business income and expenses ✓ Capital expenditure ✓ Class grades ✓ Eye color ✓ Vehicle Data and Variable 2 Types of Variables Qualitative Variable Are variables that have distinct categories according to some characteristic or attribute. If the subject of the research is classified according to gender (male or female), then the variable is qualitative. Other examples are religious preference and geographic locations. 2 Types of Variables Quantitative Variable Also known as numerical variable Are variables that can be counted or measured If the subject of the research is classified according to age, then the variable is numerical, and people can ranked in order according to the value of their ages. Other example of quantitative variables are heights, weights and body temperature. Discrete variables Continuous variables Qualitative VS Quantitative Let’s Try 3: Qualitative or Quantitative variables 1. The temperature in Antipolo, Rizal at 12:00 pm on any given day. 2. The brand of automobile driven by each faculty member. 3. Whether or not a 6-volt lantern battery is defective. 4. The weight of a lead pencil. 5. The length of time billed for a long-distance telephone call. 6. The brand of cereal children eat for breakfast. 7. The type of book taken out of the library by a student. 2 Types of Variables Quantitative Variable Also known as numerical variable Are variables that can be counted or measured If the subject of the research is classified according to age, then the variable is numerical, and people can ranked in order according to the value of their ages. Other example of quantitative variables are heights, weights and body temperature. Discrete variables Continuous variables 2 Types of Quantitative Variables Discrete variables Assume values that can be counted Exact numbers number of children in a family number of students in a classroom number of calls received by a call center each day of the month 2 Types of Quantitative Variables Continuous variables can assume an infinite number of values between any two specific values. They are obtained by measuring. They often include fractions and decimals Temperature Height Weight Discrete vs. Continuous Discrete Variable Exact Countable Continuous Variable Numbers between numbers Measurable Let’s Try 4: Discrete or Continuous 1. The number of defective computers produced by a manufacturer. 2. The weight of newborns each year in the hospital. 3. The number of siblings in a family of a region. 4. The amount of paint utilized in a building project. 5. The speed of a car.  Population Descriptive - Parameter Statistics Data Sample Inferential - Statistic Data Discrete Quantitative Variables Continuous Qualitative 4 Levels of Measurements Nominal Ordinal Interval Ratio Nominal Characterized by data that consist of names, labels, or categories only The data cannot be arranged in an ordering scheme Calculations done on these variables will be futile as there is no numerical value of the options A sample of teachers classified according to subject taught. Classifying residents according to zip code Political Party (Democratic, Republican, Independent, etc) Religion (Christianity, Judaism, Islam, etc) Martial Status (single, married, widowed, separated) Ordinal If they can be arranged in some order, but differences (obtained by subtraction) between data values either cannot be determined or are meaningless Origin of this scale is absent due to which there is no fixed start or “true zero” Classifies data into categories that can be ranked however, precise difference between the ranks do not exist Ordinal Guest speaker might be ranked as superior, average or poor Floats in a parade might be ranked as First, Second and Third Place Size of Shirt (S, M, L, XL) Interval Like the ordinal level, with the additional property that the difference between any two data values is meaningful Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving The only drawback of this scale is that there is no pre- decided starting point or a true zero value (arbitrary zero). Ranks data, and precise differences between units of measure do exist however, there is no meaningful zero Interval IQ Test do not measure people who have no intelligence but there is a meaningful difference between IQ scores Temperature 0°F does not mean no heat at all Ratio Is the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present) Differences and ratios are both meaningful Because of the existence of true zero value, the ratio scale doesn’t have negative values. Height Weight Time Salary Age  4 Levels of Measurements Nominal Ordinal Interval Ratio the data can only the data can be the data can be the data can be be categorized categorized and categorized, categorized, ranked ranked, and evenly ranked, evenly spaced spaced, and has a natural zero. ✓ City of birth ✓ Gender ✓ Top 5 Olympic ✓ Test scores (e.g., ✓ Height ✓ Ethnicity medallists IQ or exams) ✓ Age ✓ Car brands ✓ Language ability ✓ Personality ✓ Weight ✓ Marital status (e.g., beginner, inventories ✓ Temperature in intermediate, ✓ Temperature in Kelvin fluent) Fahrenheit or ✓ Likert-type Celsius questions (e.g., very dissatisfied to very satisfied) 4 Levels of Measurements Let’s Try 5: Identify the following as nominal level, ordinal level, interval level or ratio level data. 1. Flavors of frozen yogurt 2. Amount of money in savings account 3. Students classified by their reading ability: AA A BA 4. Letter grades on Homeroom grades Let’s Try 5: Identify the following as nominal level, ordinal level, interval level or ratio level data. 5. Commuting time to work 6. Ice cream flavor preference 7. Years of important historical events 8. Instruction classified as: Easy, Difficult or Impossible Learning Targets Define statistics Continuous and Discrete Differentiate types of Variables statistics. Identify four levels of Define the basic terms in measurement statistics Give examples for each level Population and Sample of measurement Parameters and Statistic Differentiate four levels of Data and Variable measurement Qualitative and Quantitative Variables