Pitt MATH 1100 - Statistics
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Statistics way to get information from data Measurements of VARIABILITY range variance standard deviation SKEWED values in a box plot when median and mean DON T line up DESCRIPTIVE STATISTICS methods of organizing summarizing and presenting data in convenient informative way graphical and numerical techniques INFERENTIAL STATISTICS drawing conclusions inferences about characteristics of populations based on sample data Confidence level proportion of times that an estimating procedure is correct Significance level measures how frequent the conclusion will be wrong in the long run DESCRIPTIVE STATISTICS involves summarizing and describing important features of the data SAMPLING completely random INTERVAL DATA best real numbers quantitative or numerical data Calculations are ALLOWED Numeric non categorical HISTOGRAM summarize data and explains probabilities SCATTAR DIAGRAM to display relationship of 2 interval variables for paired numerical data identify cause and effect Histogram skew ness histogram w long tail extending to either left or right Unimodal one peak Bimodal 2 peaks OGIVE graph of a CUMULATIVE frequency distribution Calculate relative frequencies then cumulate the values CROSS SECTIONAL DATA observations measured at the SAME point in time TIMES SERIES DATA observations measured at successive points in time graphed on a LINE CHART NOMINAL DATA values are categories qualitative or categorical marital status No Calculation allowed count frequency of each value of the variable Summarize data in a frequency distribution Lists the categories and the proportion with which each occurs CROSS CLASSIFICATION TABLE describes relationship between 2 NOMINAL variables Lists the frequency of each combination of the values Ordinal DATA categorical in nature but are in ORDER ranking system Calculations involving a ranking process are allowed Interval real numbers All calculations are valid Data may be treated as ordinal nominal Ordinal values represent the ranked order of the data Calculations based on ordering process are valid Treated as nominal NOT interval Nominal artibtrary numbers that represent categories Calculations based on the frequencies of occurrence are valid Can NOT be treated as interval ordinal When to use freq relative freq tables bar and pie charts Describe single set of NOMINAL data When to use histogram ogive stem leaf display Describe single set of INTERVAL data When to use cross classification table Describe relationship between 2 variables NOMINAL When to use a scatter diagram Describe relationship between 2 variables INTERVAL DESCRIPTIVE STATISTICS way of describing the numbers or data Measures of central location MEAN MODE MEDIAN Measures of Dispersion RANGE inter quartile range mean absolute deviation VARIANCE STANDARD DEVIATION coefficient of variation Inter quartile range IQR Q3 Q1 Helps to find outliers Measures of relative standing PERCENTILES Z SCORE Z SCORES the number of standard deviations that an observation lies from the mean PERCENTILES the Pth percentile is the value for which P of the data set are less than that value and 100 P are greater than that value Z SCORE some value x subtract the mean then divide by the standard deviation Measures of linear relationships CORRELATION COVARIENCE Scatter plots Covariance pattern of how variables move together Correlation coefficient puts large and small into perspective by restricting the domain to 1 1 CORRELATION IS NOT CAUSATION ONLY way to prove causation is through an EXPERIMENT OUTLIERS extreme values that are far not similar to the common values Value above Q3 1 5 IQR or below Q3 1 5 IQR Arithmetic mean vs median Mean is influenced by outliers MODE works with nominal data MEAN only works with interval or ordinal data STANDARD DEVIATION the square root of the population variance n 1 THE DEGREES OF FREEDOM COEFFICIENT OF VARIATION standard deviation divided by the mean Collecting data direct observation experiments and surveys Sampling cost and practicality Sample and target must be similar Simple random sampling removes bias every possible sample is equally likely to be chosen Stratified Random sampling separating the population into mutually exclusive sets or strata then drawing from each stratum Layers Cluster Sampling simple random sample of groups or clusters of elements When difficult or costly to develop a complete list of the population members SAMPLING ERROR diff between sample and population that exist b c of the observations that happened to be selected for the sample Increase sample size less error NONSAMPLING ERROR more serious Due to mistakes made in the acquisition of data or to the sample observations being selected improperly Increase sample size will NOT reduce this type of error 3 types ERRORS IN DATA ACQUISITION recording incorrect responses faulty equipment transcription mistake etc NON RESPONSE ERRORS error or bias when responses are not obtained from some members of the sample Sample observation may not be representative of target pop Response rate proportion of all people selected who complete the survey SELECTION BIAS when sampling plan is that some members of the target population cannot possibly be selected for inclusion in the sample 3 ways to assign probability to an outcome CLASSICAL APPROACH based on equally likely events RELATIVE FREQUENCY assigning probabilities based on experimentation or historical data SUBJECTIVE APPROACH assignment probabilities based on the assignor s subjective judgement Define probability here as the degree of belief that we hold in occurrence of an event Subjective probability based on past observations combined with current observations We study methods to determine probabilities of events that result from COMBINING other events in various ways COMPLEMENT EVENT Ac P A P Ac 1 Complement of A is the event of all sample points that are NOT A INTERSECTION OF EVENTS joint probability of A AND B think the small space in the middle of a venn diagram UNION OF EVENTS event containing all sample points that are in A or B or Both The event anywhere WITHIN the 2 circles of a venn diagram MUTUALLY EXCLUSIVE EVENTS the 2 events cannot occur together The circles of a venn diagram are not intersected No points in common DEPENDENT AND INDEPENDENT EVENTS MARGINAL PROBABILITIES adding across rows and down columns calculated in the margins of the table CONDITIONAL PROBABILITY determines how 2 events are related Can determine the probability of one event given the

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# Pitt MATH 1100 - Statistics

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