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# Midterm#1 Study Guide Math 243

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This 4 page Study Guide was uploaded by Elizabeth Notetaker on Wednesday April 15, 2015. The Study Guide belongs to Math 243 at University of Oregon taught by Price in Spring2015. Since its upload, it has received 540 views.

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Date Created: 04/15/15

Math 243 Midterm 1 Study Guide Chapter 1 139 An individual is an object eg person city company described by data 2 A variable is a characteristic of an individual a A categorical variable is a variable that places an individual s characteristic into one of several groups I b A quantitative variable is a variable that assigns a numerical value to a characteristic of the individual which makes sense to add or subtract 3 The distribution of a variable is what values the variable takes on and how many times It assumes those values 4 To picture a distribution we use a pie chart or bar graph for categorical variables and a histogram or stemplot for quantitative variables 5 Shape Eg sin gle peaked bimodal uniform symmetric vs skewed to the rightleft 6 Center Eg mean or median we ll calculate these in the next chapter 7 Spread Eg range minimum maximum quartiles variance standard deviation we ll calculate these in the next chapter 8 An outlier is an observation that subjectively doesn t t with the rest of the data Chapter 2 1 The strength of the mean is that it is easy to calculate even for large values of 12 Its primary weakness is that it is strongly affected by outliers 2 The median of a data set is the middle value of the data when ordered If there are an even number of elements the median is the mean of the two middlemost elements 3 The strength of the median is that it is resistant to outliers Its primary weakness is that it is time consuming to order a very large number of observations For roughly symmetric sets the mean and median are similar In skewed distributions the mean is pulled away from the median in the direction of the skew 4 The quartiles of a data set divide the data into four pieces with as close as possible to equal numbers of elements in each The five dividers which we call the venumber summary are the Min Q1 Median Q3 and Max Thus the rst quartile Q is the median of the interval Min Median and the third quartile Q3 is the median of the interval Median Max Note that the quartiles never include the median treated as its own data point in the grouping A boxplot is a visual representation of the venumber summary along the number line 5 The interquartile range is given by IQR 1 Q3 Q1The Interquartile Range Rule says that any data that fall outside of the interval Q1 15IQR Q3 15 IQR are suspected outliers This is not a catch all for outliers Chapter 3 1 The density curve of a distribution of a continuous variable is a curve such that the area under the curve and between any range of observations is the proportion of observations that fall into that range A density curve is always above the horizontal axis because negative numbers of observations don t make sense and the area underneath the curve is exactly equal to 1 because when you put all the observations together you should get 100 of the data 2 4 5 A Normal distribution has a symmetric density curve that is bellshaped According to custom we call the mean of the distribution u mu and its standard deviation 0 sigma To indicate that a random variable X has a Normal distribution we often write X NUMJ The 6895993 Rule says for a Normal distribution that approximately 68 of the observations are within one standard deviation of the mean 95 are within two standard deviations and 997 31 6 within three standard deviations of the mean The standard Normal distribution is the particular Normal distribution with mean u 0 and Standard deviation 0 1 Observations in the standard Normal distribution are typically denoted by z 2 x meanstd z score Chapter 8 M ePNH The pupulation is the group of individuals about which we want information A sample is a portion of the population that we actually gather information from A sampling design describes how to choose a sample from the population 39 Bias is the systematic tendency of a study to favor certain outcomes There are several types of blas Nonresponse is when a selected individual cannot or will not contribute to the study Callng telephone numbers at random but individuals choose not to pick up the phone Undercoverage is when some groups in the population are left out of being chosen for the sample Calling only landlines not cell phones Response is when an individual supplies incorrect information eg based on poor memory or sensrtive topic of questioningAsking questions about television viewing habits from a year ago or about underage drinking Poor wording is when the phrasing of the question either being confusing or by leading the indi vidual encourages one outcome over others Given that our country is in the deepest recession in decades how do you feel Congress has been performing its duties There are several major categories of sampling design a A voluntary response sample is when individuals choose whether or not to participate This type of sampling is often biased toward strong opinionsA booth is set up outside of a Walmart with a sign asking people to share their experience with the store Convenience sampling is when experimenters use subjective means to sample This type of b sampling is often biased toward the interviewer s prejudice in selecting the sample A researcher chooses patients for an experimental drug out of a le of acceptable candidates 0 A random sample is a sample chosen by chance There are two common types of random samples d A simple random sample SRS of size n consists of n individuals from the population chosen in such a way that every set of 11 individuals has an equal chance to be the sample actually selected e A stratified random sample is when the population is grouped and then an SRS is taken from each stratum f A multista g8 sam 1e us m p es two or Ore Organizational strategies to determine a sample 10 How to create an SR5 3 Give each a member 0f the Population a numerical label of the same length b Generate ran generator fogom dlglts 51118 Table B in the textbook pg 678 or another random number examples Your Calculator or at wwwrandomorg 395 Sample contains the md1v1duals whose labels you generated by the method in step 2 11 Strategies for sampling a Eliminate interviewerinterviewee choice in the selection process b Choose a large sample size c Make sure the individuals have few options to avoid selection 1 Be fully aware of the scope of the desired pOpulation e Deliver the questions neutrally without favoring any particular response Chapter 9 1 An observational study is a process of collecting data by polling interviewing or otherwise observing the individuals 2 An experiment is a process of collecting data by imposing treatme 3 The response variable is the variable which researchers seek to study pendent variable 4 The explanatory variable is the variable which causes change in the response variable also commonly called the independent variable Researchers may be able to adjust the explanatory variable to see how it changes the response variable Sometimes we cannot determine which of two explanatory variables is effecting the change in the response variable When such an error occurs we say that the variables are confounded A subject is an individual that is part of the sample in an experiment A factor is an explanatory variable in an experiment A treatment is an experimental condition imposed on some or all of the subjects An experimental design is an outline of the groups used and process by which these groups are determined the treatments imposed and measured results from the experiment 10 A placebo is a dummy treatment that is as far as the subjects can tell identical to the actual treatment 1 l A control group is the group of subjects that receives the placebo 12 A doubleblind is an experiment in which neither the subjects nor the experimenters interacting with the subjects know which group receives which treatment at on the individuals also commonly called the de Ell P 13 An uncontrolled experiment is an experiment without a comparative control group not recom mended 14 A randomized comparative experiment is an experiment with two or more treatments and the subjects are randomly assigned to the treatments 39 15 An experiment is randomized when subjects are assigned to treatments at random 16 A block design is when subjects with known similarities are grouped together NOT randomly and then 39 39nSide each b1 treatments mk A 313601 c 39 5 b and a type of b 7 had pan etween the two blocks Justl able heaSon to administer thae trngrrfe gsg 21111133323 Eg iiduals quot3 O 39 1H Mn oc disme a 5 t m Nomi Mm mm a 0 0amp0me S EancwaMf 1va WW W on Wqu CH 2 var We gZLXingtZl 301mm S 2 452 CMW3MB 3 lo 01 maqmung v Wquuamu W 9422ng 62 mmmmm Ma Mc zrlb39mh ssomg CH 0949qu WM Com oE ovscwanm am Mm 1 5m 15 o ohmmm a rc Min 2 71 CHEVY OE oweth Wt Mm 3 III STCWId de ValWZ oone b X 9 NU 0 2 z X quot39quotL 0quot quot 39 39 mmW iw

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