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# Statistical Methods STT 200

MSU

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This 13 page Class Notes was uploaded by Aryanna Jerde on Saturday September 19, 2015. The Class Notes belongs to STT 200 at Michigan State University taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/207818/stt-200-michigan-state-university in Statistics and Probability at Michigan State University.

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Date Created: 09/19/15

Stat 200 Sec106 Lecture Note1 05142007 CHAPTER I STATS STARTS HERE What is statistics Statistics have two different meanings In plural sense Statistics means a set of observations usually collected by measurements or counting collectively known as Data It also particular calculations made from data In singular sense Statistics refers to a group of scienti c methods used to 1 Collecting Data 2 Organizing and summarizing Data 3 Interpreting and analyzing Data 4 Making conclusion CHAPTER 2 DATA What is Data Systematically recorded information Whether numbers or labels together With context Data Table Time since Catalog last number A e purchase Area Nearest Internet of last Name Iyr days code stadium purchase CD bought Artist Katharine H 130 312 Wrigley Y 7TY734 Kansas Samuel P 24 18 305 Orange N CK245 Boston Chris C 43 368 610 Veterans 139 JKN234 Chimgn Monique D 5 413 Fenway Y 7OZRYT Garbage x x Context tells Who What When Where How and Why is measured 1 Who individuals about Whom data are collected participants respondents subjects experimental units records cases 2 What characteristics recorded about each individual variables 3 When time 4 Where place 5 How method of collecting data 6 Why purpose of study Variable Characteristic 0 what you actually measure or record Types of Variables Variables Categorical or Qualitative Quantitative or Numerical Discrete Continuous Quantitative Outcome is a number 0 height or concentration continuous can be any positive real number 0 number of owers on a plant discrete the scale is made up of distinct numbers with no gaps in between Usually a whole number but also eg grade in an MSU course 0 l 15 2 25 3 35 4 Categorical outcomes fall in to categories we can list 0 eye color blue black 0 Sometimes numbers can be used as names malel female2 0 choices on a survey never rarely occasionally often always CHAPTER 3 DISPLAYING CATEGORICAL DATA Example For each of 2201 people on the Titanic the following variables were recorded Ticket Class First Second Third Crew Survival Dead or Alive Age Adult or Child and SeX Male or Female ONE VARIABLE Who people on Titanic What Ticket Class Distribution Total Distribution of a variable is the list of possible values of the variable and corresponding relative frequencies Graphical displaying of a distribution of categorical data 1 Bar chart 2 Pie chart The Area of a bar or a slice should correspond to the frequency of a category Bar chart Pie Chart Crew 40 Frrst Second Thrrd Crew Example For each of 2201 people on the Titanic the following variables were recorded Ticket Class First Second Third Crew and Survival Dead or Alive TWO VARIABLES Who people on Titanic What Ticket Class and Survival Why did the chance of surviving depend on ticket class 202 123 Total 325 Percentages of Column 220 1 00 Ticket Clas First Second Third Crew Total Alive 202 118 178 212 710 73 622 411 252 240 323 2 Dead 123 167 528 673 1491 E 378 586 748 760 67 7 m Total 325 285 706 885 2201 1 00 1 00 1 00 1 00 1 00 202 U D s Q 123 Tc 2 E s V Total 325 Pie charts AHve Crew First Seconz Third Dead First Seconz Crew Third Segmented Bar Chart Alive Dead A distribution of one variable given value of another is called a conditional distribution Variables are independent if the conditional distribution for each category is the same as the corresponding marginal distribution CONCLUSION Survival rate and ticket class are dependent CHAPTER 4 DISPLAYING QUANTITATIVE DATA Changes in Enron s Stock prices Jan 1997 to Dec 1999 1 Jan 1 Feb 1 Mar Apr I May June luly I Augll SepL Orl Nm39 1 Der I997 SIJL I quot075 U6 J 1188 Ill 075 ml l75 069 0le 0 lb I34 1998 U78 002 244 028 222 050 206 038 45 4l2 llh 71150 999 325 334 7122 047 562 LS39 43l H7 ill72 l h 4amp2 NH Histogram Sorted data 450 325 175 159 144 122 088 088 075 072 069 050 050 038 028 022 016 003 012 034 047 062 069 075 078 081 116 147 206 222 244 328 334 412 431 562 Stemandleaf Display Sorted and rounded data 45 33 18 16 14 12 09 09 08 07 07 05 05 04 03 02 02 00 01 03 05 06 07 08 08 08 12 15 21 22 24 33 33 41 43 56 Stem Leaf 4 5 3 3 2 1 8642 99877554322 013567888 25 124 33 13 6 I UIbUJNl OO Dot Plot Individual observations are plotted as prominent dots above a line With a scale covering the range of data Example Reaction times to particular stimulus were taken on 11 individuals 155 13 15 13 13 15 24 25 25 22 215 773200 073 0 701 7 7QWV j Noemi t IgfzZ TW I WK 39 I I m arm 0 KW VI6 WFIN 02 L m I 26401 J L W R 0 abpl A Zj M35 War 7 37 77 Wquot a W M AH W 71 mng 04am a a Go 76 EAF z 50 F6p s Woe7W lt M BMWkw a 1 a NamM M 500 Hg fzf msw w 1 07 0 MS 5706086 My 9 666009 4 ij 5770 ayKJWJ M0 9 ft f pOSB39ES SUI 3 5 67 MATT01V 7amp7 EFW 87 gv wrap or 0600 Wm3 MK N ocmik Swagws a 477577100 f MAWMs CT 7753K 8f m 39NMOL F04 Eye Ry 47 gt exJog 7 V V7ON f zzowj39 4 mam7724 swamde 47 Erma 4 c7 7 CZ x 1 7 V7 PM 4Wgt 00 PM COVEEWJS maL m up 5 CoyV7 IV V VJVWOW Mare777M I6 Avab NMWW 57 WENquot 1 fig I We pggaan G39 l 7 3 35 0 4511 OK 9 mltC V 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