Week 1 Introduction to Statistics PDF

Let us START !  Chapter 1 Introduction to Statistics Definition Basic Areas of Statistics Types of Data Sets & Measurements Types of Data & Level of Measurements  Whole Unit: Learning Outcomes At the end of this chapter, the student is expe...

Let us START !  Chapter 1 Introduction to Statistics Definition Basic Areas of Statistics Types of Data Sets & Measurements Types of Data & Level of Measurements  Whole Unit: Learning Outcomes At the end of this chapter, the student is expected to answer these questions 1) What is “statistics”? 2) How to classify data? 3) What is the importance of statistical analysis? Period 1 Objective: Explain “What Statistics is?’ Success Criteria I can explain what statistics is I can use statistical terms to describe and summarize data I can evaluate data based on real-life datasets obtained from observation or experiments  Statistics - the science of collecting, organizing, analyzing, and interpreting data - set of figures or measures  Statistician - a person who collects information or one who prepares analysis or interpretations He may be a scholar who develops a mathematical theory on which the science of statistics is based.  Areas of Statistics 1. Descriptive Statistics 2. Inferential Statistics  Descriptive Statistics - deals with methods of organizing, summarizing, and presenting numerical data in a convenient form - statistician tries to describe a situation For example Getting census of the population is or of little value if it is just a mass of numerical data. It can be meaningful if it can be organized into a sort of table called the frequency distribution or of some kind of graphs.  Descriptive Statistics Descriptive statistical methods could be used to summarize the data. For example Actual sales level An average weekly sales levels, and The degree of variation from this average that weekly sales undergo  Inferential Statistics - consist of generalizing from samples to populations performing hypothesis testing, determining relationships among variables, and making predictions - main concern is to analyze the organized data leading to prediction or inferences  Inferential Statistics It implies that before carrying out an inference, appropriate and correct descriptive measures or methods are employed to bring out good results. For example Predicting the life span of a mechanical toy gun is based on the performance of several similar toy guns. Its prediction depends on the descriptive statistical tools to be undertaken.  Inferential Statistics Another example A researcher may wish to know if a new drug will be effective in reducing the number of heart attacks in men over 60 years of age. For this study, two groups of men over 60 would be selected. One group would be given the drug, and the other would be given a placebo. The number of heart attacks in men would be counted. Statistical test would then be applied.  Sample: A subset of the population used to estimate the characteristics of the entire population. Inferential Statistics: This branch of statistics is concerned with making inferences or generalizations about a population based on information obtained from a sample. Descriptive Statistics: Within the context of a sample, descriptive statistics summarize the data using measures such as the sample mean, variance, and standard deviation. Drawing Conclusions: Inferential statistics involves using these sample statistics to make predictions, estimates, or decisions about the population parameters, often with a certain level of confidence or probability. Period 2 Objective: Explain what are the meanings of sample, population, parameter, and statistic Success Criteria I can explain what are the meanings of sample, population, parameter, and statistic I can use the terms sample, population, parameters, and statistic in their right context when analyzing data I can evaluate data based on real-life sampling with true parameters and demonstrate generalizations.  Define: Basic Terms in Statistics 1. Universe 2. Variable 3. Population 4. Sample 5. Parameter 6. Statistic Online Game ! https://polar-ice.or g/polar-explorer-ad ventures/data-to-th e-rescue/activity-2- diving-into-data/m m-sorter-simulator/  Universe - the collection of things or observational units under consideration  Variable - a characteristic observed or measured on every unit of the universe  Population - the set of all possible values of the variable of interest  Sample - the portion of the population that has been selected for analysis - a subset of a population  Example Suppose we are interested in studying the factors related to the student’s performance in Math 28 at Central Philippine University. Universe: students of PPS Variables: Math 28 performance and factors such as age, grade in College Algebra, year level, gender  Example Suppose we are interested in studying the factors related to the student’s performance in Math 28 at PPS Population: ages of all students of PPS enrolled in Math 28, grades of all students of PPS enrolled in Math 28 Sample: performance or ages or grades of students in one section of Math 28  Parameter - a numerical measurement obtained using the population data set  Statistic - a numerical measurement obtained using the sample data set 16. The Union of Electrical Workers of America with 9,128 members polled 362 members about a new wage package that will be submitted to management. The population is the 362 members. True False 17. The CIA World Factbook cited these numbers for the United States: The birthrate is 13.66 births per 1,000 population. The average life expectancy for females is 81.17 years. Approximately 316.7 million persons reside in the United States. Each of these numbers is referred to as a statistic. True False 18. If we select 100 persons from 25,000 registered voters and question them about candidates and issues, the 100 persons are referred to as the population. True False 19. Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisions. True False 20. Categorizing voters as Democrats, Republicans, and Independents is an example of interval level measurement. True False 21. The order that runners finish in a race would be an example of continuous data. True False 1-3 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 22. Based on a sample of 3,000 people, the civilian unemployment rate in the United States was 5.5%. 5.5% is referred to as a statistic. True False 23. The principal difference between the interval and ratio scale is that the ratio scale has a meaningful zero point. True False 24. The branch of mathematics used to facilitate the collection, organization, presentation, analysis, and interpretation of numerical information is referred to as statistics. True False 25. The number of children in a family is a discrete variable. True False Multiple Choice Questions 26. The main purpose of descriptive statistics is to: A. Summarize data in a useful and informative manner. B. Make inferences about a population. C. Determine if the data adequately represents the population. D. Gather or collect data. 1-4 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Period 3 Objective: Differentiate between categorical and numerical data types. Success Criteria I can differentiate between categorical and numerical data I can categorize data based on their different properties and attributes I can evaluate data based on the nature of their categories in real life examples.  Types of Data or Variables 1. Qualitative Variables or Categorical 2. Quantitative Variables or Numerical  Qualitative Variables - yield categorical responses and answers to “what kind” questions, non-numerical characteristics or labels - represent differences in quality, character, or kind but not in amount Examples eye color, favorite movie, political party affiliation, blood type, brand of computer, level of customer’s satisfaction, nationality, student ID number  Quantitative Variables - yield numerical responses and answers to “how many” and “how much” questions, numerical measurements or quantities - numerical in nature and can be ordered or ranked Examples height, weight, income, resting pulse rate, number of cell phones owned, household size, number of students in a Statistics class, proportion of students who passed Math 28 last semester Classifications of Quantitative Variable 1. Discrete Variable 2. Continuous Variable  Discrete Variable - a quantitative variable that can assume a finite number or utmost countable number of values - produces numerical responses that arise from a counting process Examples number of magazine subscriber, number of typhoons, amount of cash in the cash registry, number of satisfied customers, graduates in a certain college, number of students in a classroom  Continuous Variable - a quantitative variable that can assume an infinite number of values associated with the values within a continuum or interval, depending on the precision of the measuring instrument Examples height, length of hair, length of longest long- distance call made per month, monthly charge of water consumption  Levels of Measurement Data can also be described in terms of the level of measurement attained.  Levels of Measurement 1. Nominal Scale 2. Ordinal Scale 3. Interval Scale 4. Ratio Scale  Nominal Scale - classifies data into various distinct categories in which no ordering is implied - uses numbers for the purpose of identifying name or membership in a group or category - observations can be classified and counted without particular order or ranking imposed on the data Examples blood type, course, breed of dog, shape of bacteria in a Petri dish, internet provider, political party, religion, telephone number, preferred hobbies  Nominal Scale Nominal scaling is the weakest form of measurement because no attempt can be made to account differences within a particular category or to specify any ordering or direction across the various categories. All qualitative variables are measured on a nominal scale.  Ordinal Scale - has the characteristics of a nominal scale with an additional characteristic that categories are ordered Examples UAAP basketball ranking, calamity threat level, level of performance, letter grades, ordering of food by preference, income category, birth order  Ordinal Scale Ordinal scaling is somewhat a stronger form of measurement because an observed value classified into one category possesses more of a property being scaled than does an observed value classified into another category. Ordinal scaling is still relatively weak though because no attempt is made to account for differences between the classified values.  Note!!! Data obtained from categorical variables are considered to be measured on nominal scale or on an ordinal scale.  Interval Scale - a scale of measure used for data values that are numerical - indicates an actual amount and there is equal unit of measurement separating each data, specifically equal interval Examples temperature, score, grade  Interval Scale Ratio between two data values is meaningless. This occurs when zero is an arbitrary measurement rather than actually indicating “nothing”.  Ratio Scale - the same with the interval scale - zero measurement indicates absence of the quantity being measured Examples weight, height, number of children, election votes, length, area, volume, velocity, money, duration  Note!!! Data obtained from numerical variables usually assumed to have been measured either on an interval scale or a ratio scale. These scales constitute the highest levels of measurement. They are stronger forms of measurement than an ordinal scale because you can determine not only which observed value is the largest but also by how much.  Summary Chart for the Classification of Data Variables Qualitative Quantitative (categorical) (numerical) Nominal Ordinal Discrete Continuous Interval Ratio 57