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# Basic Statistics MAT 112

GPA 3.54

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This 3 page Class Notes was uploaded by Dr. Taya Dickens on Wednesday October 28, 2015. The Class Notes belongs to MAT 112 at Utica College taught by Brad Emmons in Fall. Since its upload, it has received 18 views. For similar materials see /class/230522/mat-112-utica-college in Mathematics (M) at Utica College.

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Date Created: 10/28/15

De nitions Be able to classify variables as either H a Population vs Sample b Quantitative vs Qualitative c Discrete vs Continuous Be able to take raW data and make a frequency distribution table and a histogram E0 EX The ages of 20 children are given as followed 7456757463 9775474338 a Create a frequency distribution table b Create a histogram for the data CA3 Finding mean median and mode for ungrouped data a Mean and Variance for Population data 2 2 2 7 A 2 2 l 02 I N I N N b Mean and Variance for Sample data 7 Ex 2 2127Ez2 I7 3 n n71 Finding mean and standard deviation for grouped data F Commuting Time in minutes f 0 to less than 10 3 10 to less than 20 5 20 to less than 30 8 30 to less than 40 40 to less than 50 N 5 Stem and Leaf displays Given raW data make a stem and leaf display Also given a stem and leaf display nd the raW data Example Create a stem and leaf display for the following data 17 43 53 26 34 35 27 42 26 33 19 47 27 25 41 37 14 32 33 18 Example The following is a stem and leaf display Write the data set that is represented by the display 02 3 3 4 5 2 3 35 2 4 6 2 68 1 4 2 6i Chebyshev7s Theorem and Empirical Rule a Chebyshev7s Theorem For any k 2 1 at least 1 1 P of the values are within k standard deviations of the mean b Empirical Rule For a data set with a bellshaped distn39butz39zm 0 Approximately 68 percent of the data lie within 1 standard de viation of the mean 0 Approximately 95 percent of the data lie within 2 standard de viations of the mean 0 Approximately 9917 percent of the data lie within 3 standard deviations of the mean 7 Probability Experiments Outcomes Sample Spaces Conditional Prob ability lntersections and Unions of Events Example A A Total B 3 4 F 6 8 Total a Find PA PB PF PA WP PA l B PA1B PA U B b Are the events A and B independent c Are the events A and B mutually exclusive Example Toss a coin three times Let A be the event that there was at least one head and let B be the event there was exactly one taili a Find the sample space for this experiment 00 b Find PAi c Find PBi d Find PA O B e Find PA U B Example It is known that 75 percent of the population has mad cow dis ease An experiment consists of selecting two members of the population and noting whether or not they have mad cowl a Find the probability exactly one selected member has mad cowl b Find the probability both selected members have mad cowl i Probability Distribution Functions of a Discrete Random Variable Example In the preVious experiment7 let I be the discrete random vari able that counts the number of people that we selected who have mad cow disease Find the probability density function for this random variable 1 Find the mean and standard deViation for this probability density

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