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Chapter 1-3 Notes Statistics Chapter 1 - Intro to Statistics 1.2 Types of Data - What’s the difference between discrete and continuous data? Give an example of each. - Discrete: quantities are countable wholes - Continuous: quantities are divisible into fractions. - Examples: eggs and milk - What’s the difference between a population parameter and a sample statistic? Give an example of each. - A population parameter measures a characteristic of a whole population. It (usually) cannot be measured directly. - A sample statistic is a measurement of a sample, which , of course, can be measured directly. - Examples: population proportion p and sample proportion p̂ population mean and sample mean x - What's the difference between Descriptive Statistics and Inferential Statistics - Descriptive Statistics: use stats to describe a data set. For example, sample mean x . - Inferential Statistics: use sample stats to infer something about a population parameter. For example, the hypothesis test TTest uses the sample stats x , s, and n to test claims made about a population mean . - What are the four levels of measurement? Give examples of each. - nominal (eye color), ordinal (excellent, good, poor,..), interval (temperatures), ratio (hieght) 1.3&1.4 Sampling - When you take a simple random sample of size n, you sample in such a way that you give all possible samples of size n the same chance of being selected. - Random Sample of size n: I gave each of the n individuals an equal chance of being chosen. - Simple Random Sample of size n: I gave each possible group of size n the same chance of being chosen. - Other ways sampling can go bad, like Volunteer Response cf. pg 12. Chapter 2 - Summarizing and Graphing Data 2.2 - - Frequency Distributions What is a frequency table in your own words: A frequency table is a table with Classes in the first column and second column has frequencies (number of times data in that class is in the data set) Know how to construct a frequency table, as in problems 17 and 19. What’s the difference between a frequency table and a relative frequency table? A relative frequency table has percentages instead of frequencies. - 2.3 - What do you call the groups into which data is grouped in each row of a frequency table? (ans. Classes, Categories) Histograms What’s the relationship between a frequency table and it’s histogram? A histogram is a picture of a frequency table. Know how to construct histogram from a frequency table, as in the homework. Chapter 3 - Statistics for Describing, Exploring, and Comparing Data (Sample Stats) - 3.2 - - - 3.3 - - Name the three main characteristics of a data set: Center, Variation, Distribution (cf. pg 48) For each of the three main characteristics of a sample data set, name a sample stat or other descriptive technique that measures it. o Center: mean (or median), o Variation: standard deviation (not really another choice), o Distribution: histogram, box plot, bell curves Measures of Center Explain what a “measure of center” attempts to describe about a data set. o One number that represents the whole data set. Name four measures of center (ans. Mean, Median, Mode, Midrange). Explain the difference between each of them. What are their relative strengths and weaknesses? See Fig 3-1, pg 93 o Mean: weakness is that it’s affected by outliers o Median: is not o Mode: is only one you can use on Nominal data (think the average eye color of the class) What calculator function do we use to calculate measures of center? o 1VarStats Which two measures of center are calculated by this function and which two are not? o Mean, median o Not mode and midrange Explain the difference in how you use the calculator for calculating the mean of a list of raw data as opposed to data summarized in a frequency table. o Use two lists instead of one. 1VarStats L1 L2 T/F There is always a mode. (False) Measures of Variation Explain what a “measure of variation” attempts to describe about a data set. o Spread-out-ness, fluctuation, range, What calculator function to we use to calculate measures of variation? o 1 VarStats Mr Johnson’s two facts about standard deviations. (the two important interpretations of the standard deviation) 1. Most of the data is within one standard deviation of the mean. 2. Any data outside of two standard deviations away from the mean is considered unusual. Coefficient of Variation (cf pg 114, Hw 3.3: 21,23) 3.4 - - - Measures of Relative Standing, Box Plots What is a z score? xx o z s What is the Five Number Summary? (ans. Min, Q1, Med, Q3, Max) What calculator function to we use to calculate the Five Number Summary, 1VarStats How do you construct a box plot? o Make it to scale! o If you have two box plots, put one over the other. Fill in the blank: The 5 number summary indicates the ___distribution____ of the data.