One common wrong answer: 1 5, as the 5 possibilities for the number of boys are not equally likely. are licensed under a, Definitions of Statistics, Probability, and Key Terms, Data, Sampling, and Variation in Data and Sampling, Frequency, Frequency Tables, and Levels of Measurement, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, Histograms, Frequency Polygons, and Time Series Graphs, Independent and Mutually Exclusive Events, Probability Distribution Function (PDF) for a Discrete Random Variable, Mean or Expected Value and Standard Deviation, Discrete Distribution (Playing Card Experiment), Discrete Distribution (Lucky Dice Experiment), The Central Limit Theorem for Sample Means (Averages), A Single Population Mean using the Normal Distribution, A Single Population Mean using the Student t Distribution, Outcomes and the Type I and Type II Errors, Distribution Needed for Hypothesis Testing, Rare Events, the Sample, Decision and Conclusion, Additional Information and Full Hypothesis Test Examples, Hypothesis Testing of a Single Mean and Single Proportion, Two Population Means with Unknown Standard Deviations, Two Population Means with Known Standard Deviations, Comparing Two Independent Population Proportions, Hypothesis Testing for Two Means and Two Proportions, Testing the Significance of the Correlation Coefficient, Mathematical Phrases, Symbols, and Formulas, Notes for the TI-83, 83+, 84, 84+ Calculators, https://openstax.org/books/introductory-statistics/pages/1-introduction, https://openstax.org/books/introductory-statistics/pages/1-1-definitions-of-statistics-probability-and-key-terms, Creative Commons Attribution 4.0 International License, all students who attended the college last year, the cumulative GPA of one student who graduated from the college last year, a group of students who graduated from the college last year, randomly selected, the average cumulative GPA of students who graduated from the college last year, all students who graduated from the college last year, the average cumulative GPA of students in the study who graduated from the college last year. We want to know the average (mean) amount of money first year college students spend at ABC College on school supplies that do not include books. This wide-ranging, jargon-free dictionary contains over 2,000 entries on all aspects of statistics including terms used in computing, mathematics, operational research, and probability, as well as biographical information on over 200 key figures in the field, and coverage of statistical journals and societies. 68 0 obj Found inside – Page 343Glossary. of. Terms. SECTION I 1. Cumulative distribution function, cdf, of a random variable: A function F defined ... Example 1: X has the pdf defined by f ( x ) = 0 ; x <−2 = 0.25 ; −2 ≤ x ≤ 2 = 0 ; x > 2 See Figure below. f(x) ... 36 0 obj Probability implies 'likelihood' or 'chance'. Example. Statistics are part of our everyday life. The words "mean" and "average" are often used interchangeably. Q-notation. You should be familiar with the basic tools of the gambling trade: a coin, a (six-sided) die, and a full deck of 52 cards. The distinction between a population together with its parameters and a sample together with its statistics is a fundamental concept in inferential statistics. 1. Want to cite, share, or modify this book? 2 . Probability Theory: STAT310/MATH230By Amir Dembo The answers were 1, 0, 1, 3, and 4 glasses of milk. 996 However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails.
We randomly surveyed 100 first year students at the college. >> If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three (your mean score would be 84.3 to one decimal place).
In itself, probability theory has some basic objects and their relations (like real num- You need at most one of the three textbooks listed below, but you will need the statistical tables. (Population and Samples) Recall that the s-quantile for θ is the value q s with P (θ ≤ q s) = s. So for s ≤ t, the amount of probability between the s-quantile and the t-quantile is just t − s. In these terms, a p-probability interval is any interval [q s,q t] with t − s = p. Example 2. Note: In mathematics, an axiom is a result that is accepted without the need for proof. The theory of probability has always been associated with gambling and many most accessible examples still come from that activity. For example, consider the following data: 5; endobj A study was conducted at a local college to analyze the average cumulative GPA’s of students who graduated last year. Definitions of Statistics, Probability, and Key Terms. The parameter is the proportion of driver dummies (if they had been real people) who would have suffered head injuries in the population. The data are either: yes, was involved in one or more malpractice lawsuits, or no, was not. Do the following exercise collaboratively with up to four people per group. All other events have a probability that lies somewhere in between these two values. The average length of time (in months) AIDS patients from the sample live after treatment. The statistic is an estimate of a population parameter. /Length 327
76 0 obj 2 Explain how samples and populations, as well as a sample statistic and population parameter, differ. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. A stockbroker uses probability to determine the rate of return on a client’s investments. p ( A) Read: "the probability of event A ". The science of statistics deals with the collection, analysis, interpretation, and presentation of data. �Wx����6I�)O�{�-�����U����u��U��g� �D�}!БTd��f�y*�f(�Qlvg���;�l�!-��������>,ۮ�OAȮ��|y�G�nC��}B�'��MZk�^����)���F�$�\�����m�U|�DzI��_����y�0y�c�(ܸ(�&\H�� s�A��&z�8*�u>��͇KR|H������sݹ���W;}i This is a textbook for an undergraduate course in probability and statistics. Know the definitions of sample space, event and probability function. << /S /GoTo /D (section.2.3) >> How to use probability in a sentence. A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Hence the value of probability ranges from 0 to 1. Introduction to CHAPTER1 Statistics LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Distinguish between descriptive and inferential statistics. endobj Two words that come up often in statistics are mean and proportion. Population_____ 2. For example, to explain a boxplot, one must already know the meaning of a mean, median, a quartile, and an outlier. Statistic involving organizing, summarizing, and displaying data.
The understanding must come from you. 1 is the probability of something certain . For example, consider the following data: The dot plot for this data would be as follows: Does your dot plot look the same as or different from the example? 2 is the sample variance) SS sum of squares . in strict mathematical terms, a probability space consists of: a sample space Ω, a set Fof subsets of Ω that will be called the events, a function P that assigns a probability to each event and that must obey certain axioms.
(Probability of Events) 99 0 obj << (and in statistics in general) sampling with replacement,,,,, . The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in the population. endobj In addition, it defines symbols for a limited number of these terms. We could do some math with values of X (calculate the average number of points earned, for example), but it makes no sense to do math with values of Y (calculating an average party affiliation makes no sense). Found inside – Page 540chip reliability is defined as a probability, implying that quantifying it must involve statistical methods. ... Density Function (pdf) The failure probability density function 540 11 Chip Reliability 11.2 Definition of Terms and Basic ... Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. All definitions agree on the algebraic and arithmetic procedures that must be followed; hence, the definition does not influence the outcome. The average value is 4. All one needs to do is examine There are various terms utilised in the probability and statistics concepts, Such as: Random Experiment; Sample Sample Numerical variables take on values with equal units such as weight in pounds and time in hours. From the sample data, we can calculate a statistic. Fill in the letter of the phrase that best describes each of the items below. 29 0 obj endobj Spell. We see and use data in our everyday lives. A probability measure is a function de ned over the sets in a . If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. Users may download the statistics & probability formulas in PDF format to use them offline to collect, analyze, interpret, present & organize numerical data in large quantities to design diverse statistical surveys & experiments. as the probability of error, and deduce thresholds based on it. r Pearson product-moment sample correlation coefficient . One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The statisti-cian makes a guess (prior distribution) and then updates that guess with the data. Found inside – Page vThe pdf in ( 1.6.9 ) gives an example of a continuous random variable whose df is not differentiable at countably infinite number of points . Example 1.6.5 Consider the function f ( x ) defined as follows : f ... Effective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination of the data. 64 0 obj This brings us to the question of computing probabilities in various situations. The fraction is equal to 0.498 which is very close to 0.5, the expected probability.
We see and use data in our everyday lives. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. In a later chapter, we will use the sample statistic to test the validity of the established population parameter. Y is a categorical variable. The sample is the 75 cars, selected by a simple random sample. zve�V��n�$�C�U��BⲴ�=H�*����Srj�6� ������. See the below table to understand them. 69 0 obj Computing the single number $ 8, 357 to summarize the data was an operation of descriptive . The variable X = the number of medical doctors who have been involved in one or more malpractice suits. 1 INTRODUCTION 2 Example 1.2. It helps to list the various probability terms and definitions used before going in-depth. For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Terms Used in Probability and Statistics. 1.5 Data Collection Experiment. You might use probability to decide to buy a lottery ticket or not. 1.1 Definition of Statistics, Probability, and Key Terms. Sample _____ 5. Examples are: 2 hours, 5 hours, and 7.5 hours –>. Probability questions arise naturally in many contexts; for example, "What is the probability of getting five numbers plus the bonus ball 1.1 Definitions of Statistics, Probability, and Key Terms. modern statistical and statistics-related concepts, then look no further than this dictionary. With this example, you have begun your study of statistics. Look up Appendix:Glossary of probability and statistics in Wiktionary, the free dictionary. As an Amazon Associate we earn from qualifying purchases. 80 0 obj The questions above ask you to analyze and interpret your data. 2 The substitution of one word for the other is common practice. To study the population, we select a sample. << /S /GoTo /D (chapter.1) >>
The probability of the union of any set of two by two incompatible events is the sum of the probabilities of the events. In addition, short biographies of over 100 important statisticians are given. Definitions provide enough mathematical detail to clarify concepts and give standard formulae when these are helpful. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average (mean) number of glasses of milk college students drink per day. << /S /GoTo /D (section.2.5) >> PLAY. 7;
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The calculations can be done using a calculator or a computer. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. /Subtype /Image Probability is a mathematical tool used to study randomness. The population is all cars containing dummies in the front seat. endobj proportion of variance in y accounted for by x . Predictions take the form of probabilities. some working knowledge of other terms, not all of which can be defined at the same time. Associate Professor. Entries are provided for standard and specialized statistical software. 8; We could do some math with values of X (calculate the average number of points earned, for example), but it makes no sense to do math with values of Y (calculating an average party affiliation makes no sense). Probability of any (Boolean) expression involving events A,B,C,.can be always converted to a linear combination of probabilities of the individual events and their simple (non-complemented) intersections (A∩B,A∩B∩C,etc.) Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Chapter 5 Random Variables and Their Probability Distributions 5.1 Random variables 178 5.2 Probability Distribution of Discrete random variable 181 5.3 The Mean and Standard Deviation for Discrete random Variable 186 5.4 Application to the Random Variable 194 References ( 211 ) /Appendix A - Statistical Tables ( 213 ) /Dictionary ( 231 ). We are interested in both the sample statistic and the population parameter in inferential statistics. Used For. We recommend using a /Parent 107 0 R In general, statistics is a study of data: describing properties of the data, which is called descriptive statistics, and drawing conclusions about a population of interest from information extracted from a sample, which is called inferential statistics. 96 0 obj However, in practice among non-statisticians, “average” is commonly accepted for “arithmetic mean.”. Glossary of Key Data Analysis Terms Levels of data Nominal Variable - A variable determined by categories which cannot be ordered, e.g., gender and color. << /S /GoTo /D (section.1.3) >> It deals with the chance (the likelihood) of an event occurring. endobj endobj Definitions of Statistics, Probability, and Key Terms, Data, Sampling, and Variation in Data and Sampling, Frequency, Frequency Tables, and Levels of Measurement, Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs, Histograms, Frequency Polygons, and Time Series Graphs, Independent and Mutually Exclusive Events, Probability Distribution Function (PDF) for a Discrete Random Variable, Mean or Expected Value and Standard Deviation, Discrete Distribution (Playing Card Experiment), Discrete Distribution (Lucky Dice Experiment), The Central Limit Theorem for Sample Means (Averages), A Single Population Mean using the Normal Distribution, A Single Population Mean using the Student t Distribution, Outcomes and the Type I and Type II Errors, Distribution Needed for Hypothesis Testing, Rare Events, the Sample, Decision and Conclusion, Additional Information and Full Hypothesis Test Examples, Hypothesis Testing of a Single Mean and Single Proportion, Two Population Means with Unknown Standard Deviations, Two Population Means with Known Standard Deviations, Comparing Two Independent Population Proportions, Hypothesis Testing for Two Means and Two Proportions, Testing the Significance of the Correlation Coefficient, Mathematical Phrases, Symbols, and Formulas, Notes for the TI-83, 83+, 84, 84+ Calculators. 2. 24 0 obj Statistics is a study of data: describing properties of data (descriptive statistics) and drawing conclusions about a population based on information in a sample (inferential statistics). Why or why not? It can be shown on a line. Statistical inference uses probability to determine how confident we can be that our conclusions are correct. all voters in the politician’s district a random selection of voters in the politician’s district the proportion of voters in this district who think this politician is doing a good job the proportion of voters in this district who think this politician is doing a good job in the sample X = the number of voters in the district who think this politician is doing a good job Yes, he is doing a good job. We randomly survey 100 families with children in the school. The parameter is the average (mean) amount of money spent (excluding books) by first year college students at ABC College this term. It is important to note the consequences of the definition: 1.
Core Statistics is a compact starter course on the theory, models, and computational tools needed to make informed use of powerful statistical methods. Give examples where appropriate. This Eighth Edition continues to focus students on two key themes that are the cornerstones of this book's success: the importance of looking at the data before beginning a hypothesis test, and the importance of knowing the relationship ... For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Variable _____ 6. In your classroom, try this exercise. 53 0 obj 45 0 obj (Bayes' Theorem) X, Y, Z, T. Random variables. Probability, Statistics and Estimation Propagation of Uncertainties in Experimental Measurement (Short Edition) Mathieu ROUAUD Physics and Chemistry Lecturer in Preparatory Classes for the Engineering Schools. With that preface out of the way, we can now get down to the business of discussing, "What do the terms measurement and statistic mean?" and "Why should we study measurement and statistics?". The variable X = whether an individual doctor has been involved in a malpractice suit. (Logistic Regression) Three of those students spent $150, $200, and $225, respectively. Have class members write down the average time (in hours, to the nearest half . 89 0 obj Determine what the key terms refer to in the following study. In your classroom, try this exercise. /Resources 100 0 R Probability: Terminology and Examples Class 2, 18.05 Jeremy Orloff and Jonathan Bloom. This text offers a sound and self-contained introduction to classical statistical theory. Source: NIH.GOV. (Questions on Samples) 81 0 obj Mean and proportion are discussed in more detail in later chapters. One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. Statistics and Probability is a fourth mathematics course option for students who have completed Algebra II. consent of Rice University. %PDF-1.4 In your study of statistics, you will use the power of mathematics through probability calculations to analyze and interpret your data. /Filter /FlateDecode In a later chapter, we will use the sample statistic to test the validity of the established population parameter. endobj endobj The calculations can be done using a calculator or a computer. We know that there are more statistics terms which you can find in statistics glossary i.e., various types of tests in statistics, ANOVA, MANOVA, theorems, and lots more. Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter. r . It deals with the chance of an event occurring. The actual outcome is considered to be determined by chance.. The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. S sample standard deviation (S . Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors.
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