statistics chapter 1 introduction to statistics. keep this in mind statistics have very logical...
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- Statistics Chapter 1 Introduction to Statistics
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- Keep this in mind Statistics have very logical answers. Statistics can be linked with psychology and sociology Keep an open-mind, there are always 2 sides to a coin (positive and negative)
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- Quick Talk 1 out of 3 people cheat in a relationship Discuss this statement What does it mean? Do you believe it? Why or why not?
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- Based on your discussion, why do you think its important to know about statistics?
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- Potential answers Know how authentic the statement is Dont get cheated or tricked on Know where the data comes from Know how effective something is
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- What is statistics? Statistics: the study of how to collect, organize, analyze, and interpret numerical information from data
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- So then, what is needed? Individual: people or objects included in the study Variable: characteristic of the individual to be measured or observed
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- Quick Talk Think about dating. What variables do people look for when finding a boyfriend or girlfriend? List them
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- Variable comes in two types Quantitative variable: has a value or numerical measurement for which operations such as addition or averaging make sense (usually has numbers) Qualitative variable: describes an individual by placing the individual into a category or group such as male or female
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- Base on your list, identify them as quantitative or qualitative.
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- Sample Answers Age (quantitative) Weight (quantitative) Height (quantitative) Race (qualitative) Income (quantitative) Looks (qualitative) Body type (qualitative) Personality (qualitative)
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- Data Population data: data from every individual of interest Sample data: data from only some of the individual of interest
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- Quick Talk Compare the definition. Which type is more probable? Why?
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- Parameter: a numerical measure that describes an aspect of a population Statistic: numerical measure that describes an aspect of a sample
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- Easy way to remember Population with parameter Sample with statistic
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- Group work: Example #1 A car dealer wants to know what type of car people drive in the desert. He sent out 5000 surveys to random people living in the desert. A)identify the individual of study and the variable B)do the data comprise a sample? If so, what is the underlying population? C)is the variable qualitative or quantitative? D)Identify a quantitative variable that might be or interest E) Is the random sample a statistic or a parameter?
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- Answer A) individual: people in the desert Variable: car B) The data comprise a sample of the population of all people living in the desert C) qualitative D)Income, age E) statistic- computed from sample data
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- Example #2 Television station QUE wants to know the proportion of TV owners in Virginia who watch the stations new program at least once a week. The station asked a group of 1000 TV owners in Virginia if they watch the program at least once a week A)identify the individual of study and the variable B)do the data comprise a sample? If so, what is the underlying population? C)is the variable qualitative or quantitative? D)Identify a quantitative variable that might be or interest E) Is the random sample a statistic or a parameter?
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- Levels of Measurement Nominal level of measurement: applies to data that consists of names, labels or categories. There are no implied criteria by which the data can be ordered from smallest to largest Ordinal level of measurement: applies to data that can be arranged in order. However, differences between data values either cannot be determined or are meaningless Interval level of measurement: applies to data that can be arranged in order. In addition, differences between data values are meaningful Ratio Level of measurement: applies to data that can be arranged in order. In addition, both differences between data values and ratios of data values are meaningful. Data at the ratio level have a true zero. (Means zero means something)
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- Example: Identify what level of measurement A)Taos, Acoma, Zuni, and Cochiti are names of four Native American pueblos from the population of names of all Native American pueblos in Arizona and New Mexico B) In a high school graduating class of 600 Students. Jeff ranked 1 st, Melissa ranked 38 th, Patrick ranked 150 th, Ashley ranked 3 rd, where 1 is the highest rank C) Body temperatures of trout in the Yellowstone River D) Length of shark swimming in the Pacific Ocean
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- Answer A) nominal B) ordinal C) interval D)ratio
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- Example #2 Name the levels of measurement A) My name is Mr. Liu B) I am 28 years old C) Highschool 1999-2003 College 2003-2007 Masters 2007-2008 D) I make $35,000 after tax E) I ranked 100th in highschool, 58 th in college, 27th in Masters F) Some of my friends name are Michael, Katherine, Patrick, Ashley, Sarah, Mya, Chris. G) I am 58
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- Answers A) Nominal B) Ratio C) Interval D) Ratio E) Ordinal F) Nominal G) Ratio
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- Homework Practice Pg 10-11 #1-13 odd
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- Quick Talk Mr. Liu looked at the first 15 male students grades (which averages to a C) and made conclusion that of all the students in the school should have a C average. Discuss why this statement might not be correct. What is wrong with this study?
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- Things to remember If there is a study or data collect, it can not be BIASED in any way. You need to have a decent sample size and fair randomness to it. Fair = equal chance
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- 1 st type of data collection Simple random sample: Simple random sample of n measurements from a population selected in a manner such that every sample of size n from the population has an equal chance of being selected. Basically, everything has the same chance of getting selected.
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- Simple random sample example If I were to assign a number to each of the students here. (40 students) If I were to randomly choose 5 numbers, would the number 7 as likely to be selected as number 37? Could all 5 numbers be all odd? Could it ever be 27,28,29,30,31?
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- How to Draw a Random Sample 1) Number all members of the population sequentially 2) Use a table, calculator, or computer to select random numbers from the numbers assigned to the population members 3) Create the sample by using population members with numbers corresponding to those randomly selected
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- Read Example 3 in pg 13 Random-Number Table It is one of the way to create randomness in terms of number It is called a simulation
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- Another way Random Integer (randInt): Calculator TI83, TI84 Go to MATH Slide over to PRB Choose #5 It should show randInt( If you want ONE random number out of total of 500, you should type randInt(1,500) This will give you a random number between 1 and 500 If you want 30 random numbers out of total of 500, you should type randInt(1,500,30)
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- 2 nd type of data collection Simulation (usually with number): a numerical facsimile or representation of a real-world phenomenon Note: Productive in studying nuclear reactors, cloud formation, cardiology, highway design, production control, shipbuilding, airplane design, war games, economics, and electronics.
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- Quick Talk: Why do you think it is important to use simulation as a data collection method? (think about the application field we just discussed)
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- Group Activity In your group, create a sample simulation of a coin- tossing event 10 times One person will record One person will use a coin (head or tail) One person use calculator (1=head, 2=tail) One person use the table from the back of the book (odd=head, even=tail) You should have a total of 30 trials. Answer this question: What is the theoretical probability of getting head? What is experimental probability of getting head?
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- Answer Theoretical probability: 50% Experimental probability: depends on your group
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- Sampling: Different ways to create randomness Stratified sampling: Divide the entire population into distinct subgroups called strata. The strata are based on a specific characteristic such as age, income, education level, and so on. All members of a stratum share the specific characteristic. Draw random samples from each stratum Systematic sampling: Number all members of the population sequentially. Then, from a starting point selected at random, include every kth member of the population in the sample Cluster sampling: Divide the entire population into pre-existing segments of clusters. The clusters are often geographic. Make a random sel
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