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# Statistics for Business and Economics Notes- Weeks 4 STAT 1051

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This 3 page Class Notes was uploaded by Oya Zaimoglu on Sunday February 21, 2016. The Class Notes belongs to STAT 1051 at George Washington University taught by Zhang, P in Fall 2015. Since its upload, it has received 43 views. For similar materials see Introduction to Business and Economic Statistics in Statistics at George Washington University.

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Date Created: 02/21/16

Statistics Week 4 Aids to the Interpretation of Box Plots 1. The line (median) inside the box represents the “center” of the distribution of data. S= {1, 3, 5, 6, 10, 12, 68} Median: 6 Q U : 12 QL : 3 *IQR= Inner Quartile Range= QU−Q L 2. Examine the length of the box. The IQR is a measure of the sample’s variability and is especially useful for the comparison of two samples. 3. Visually compare the lengths of the whiskers. If one is clearly longer, the distribution of the data set is probably skewed in the direction of the longer whisker (top longer- right skew; bottom longer-left skew). 4. Analyze any measurements that lie beyond the fences. Example: Mean= $64,000 z-score= 57,000– 64,000 = -3.5 2000 Standard Deviation= $2000 Salary= $ 57,000 *her salary is 3.5 below the mean. Events, Sample Spaces, and Probability General Idea: Probability is the reverse of statistics. In probability, we use information about the population to infer the probable nature of the sample. Experiment: an act or process of observation that leads to a single outcome that cannot be predicted with certainty. Sample Point: is the most basic outcome of an experiment. Probability (chance/odd): is a number between 0 and 1 which measured the likelihood that the outcome will occur when the experiment is performed. Sample Space: collection of all possible sample points. Venn Diagrams: graphical representation of sample space. The sample space is shown as a closed, figured, labeled S, containing all possible sample points. Each sample point is represented by a solid dot (i.e. a “point”) and labeled accordingly. Probability Rules for Sample Points 1. All sample point probabilities must lie between 0 and 1. 2. The probabilities of all sample points within a sample space must sum to 1. Probability of an event: specific collection of sample points. The probability of an event A is calculated by summing the probabilities of the sample points in the sample space for A. 1. Define the experiment: describe the process used to make an observation and the type of observation that will be recorded. 2. List the sample points 3. Assign the probabilities to sample points. 4. Determine the collection of sample points contained in the event of interest. 5. Sum the sample point probabilities to get the probability of the event. Determine the number of sample points 1. Develop a counting system 2. Use combinatorial mathematics Combinations Rule Suppose a sample of n elements is to be drawn without replacement from a set of N elements. Then the number of 2 N ¿n different samples possible is denoted by ¿ ) and is equal to N ! n!(N−n)! Union: the union of two events A and B is the event that occurs if either A or B (or both) occurs on a single performance of the experiment. We denote the union of events A and B by the symbol A U B. A U B consists of all the sample points that belong to A or B or bot. Intersection: The intersection of A and B is the event that occurs if both A and B occur on a single performance of the experiment. Complementary Events: the complement of an event B is the event that does not occur- that is, the event consisting of all sample points that are not in event A. We denote c complement of A by A . Rule of Complements: The sum of the probabilities of complementary events equals 1; that is P(A) + P( Ac ) = 1 Why? Because the total probability of all sample points in a sample set needs to be 1, and this set if the union. Alternative Formula: We can calculate P(A) by using the relation c P(A)=1-P( A ) 3

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