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# Mid term study guide MAT 122 - M100

Syracuse

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## Popular in Probability and Statistics for the Liberal Arts II

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This 6 page Study Guide was uploaded by Ishaq Sekalala on Monday October 19, 2015. The Study Guide belongs to MAT 122 - M100 at Syracuse University taught by Staff in Fall 2015. Since its upload, it has received 106 views. For similar materials see Probability and Statistics for the Liberal Arts II in Mathematics (M) at Syracuse University.

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Date Created: 10/19/15

Math Mid term Study guide Given a small sample space nd x bar szand S X bar is simply the arithmetic average Summation of Xnx bar 5 is the sample standard deviation It is the square root of n summation of x2summation of x 2 n nl S2 is the variance and it is simply a squaring of the sample standard deviation Given a large sample spacePopulation sample space Mew is population mean Summation of XN N being the number of data values in a population Sigma is the population deviation Square root of the summation ofxmew 2N Sigma2 is the population variance and it is simply squaring of the population standard deviation Median Quartiles lnterquartile range amp the 5 number summary 0 One quarter25 of the data falls below the rst quartile Two quarter 50 of the data falls below the 2ml quartile 0 Third quarter 75 of the data falls below the 3ml quartile Five number summaryMin Q1 Median Q3 Max Two associated Measures of spread lnterquartile range lQRQ3Ql RangeMaximum data valueMinimum value Maximum value mean 2 x standard deviation Minimum value mean 2 x standard deviation Box plot 0 Box amp whisper plot is a visual graphical display of the 5 number summary 0 Box extends from Ql toQ3 0 Line cutting through the box is at the median 0 Line whiskers extend from the box to the minimum and to the maximum Outliers If a data point is smaller than Ql15 x IQR we will consider it to be an outlier If a data point is bigger than Q315 x IQR we will consider it to be an outlier Extreme values Median is not overly in uence or not at all by extreme values in the datalj Median is a resistant measure of center Sample mean is in uenced by extreme values gt sample mean is not a resistant measure of center Rightly skewed Medianltmean The mean will be bigger than median as mean gets pulled up to the right Left skewed meanltmedian Mean will be smaller than the median mean gets pulled down to the left Roughly symmetric meanmedian 68 95 997 rule For bell shaped symmetrical data Roughly 68 of the data would fall within one standard deviation of the mean x bar plus or minus one standard deviation Roughly 95 of the data would fall within two standard deviation of the meanx bar plus or minus two standard deviations Roughly 997 of the data would fall within three standard deviations of the meanx bar plus or minus three standard deviations An outlier would lie outside of x bar plus or minus 3 standard deviations Chebyshev s theorem for data that isn t bell shaped The proportion of any set of data lying within K standard deviation of the mean is always at least 1 1K2 where K is any positive number greater than 1 For K2 and K3 we get the following statements 1122 we get 114 we get 34 or 75 of all values lie within 2 standard deviations of the mean 1132 we get 119 we get 89 or 89 of all values lie within 3 standard deviations of the mean Z score of the sample Z score Data point meanstandard deviation Z score of the population Z score data point mew sigma population deviation Finding the Z score is also referred to as standardizing the value Percentiles Ql 1St quartile 25th percentile Median Q2 2 dquartile 50th percentile Q3 3ml Quartile 75th percentile Sample space set of all possible outcomes Event any subset of the sample space Event has only one outcome we call it a simple event Relative frequency approximation of probability conduct a procedure and count the number of times that event A actually occurs Based on these actual results P A Number of times A occurred number of times the procedure was repeated Classical approach to probability requires equally likely outcomes assume that a given procedure has n different simple events and that each of those simple events has an equal chance of occurring lf event A can occur in s of these n ways then P A Number of ways A occur number of different simple events sn Complimentary events A compliment of at least one something is none of something We use not A to indicate that A does not occur Either A occurs or it does not occur P A or not A P A P not A 1 P NOT A l P A P A lP NOT A Formal addition rule PAUBPA PB PAand B Where P A and B denotes the probability that A and B both occur at the same time as an outcome in a trial of a procedure Disjoint or mutually exclusive events cannot both occur at the same time They do not overlap Eg cannot be both a registered democrat and republican NONE DISJOINT events are randomly selecting someone taking stats and a female They overlap Multiplication Rule P A X P BA Independence of events A amp B are independent if one of the events happening doesn t in uence the other P AB what is the probability of A happening given that B already happened Eg two dies are independent of each other Coins tossed are independent of each other Picking bails out of a bag with replacement Dependent events lfA happened B couldn t happen and vice versa Independence can t be seen with Venn diagrams Permutation N total of items out of which we are picking we want to pick K items order matters repeats are not allowed Eg Password PINS Combination N total of items out of which we are picking we want to pick K items with the order not mattering and repeats not allowed

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