Descriptive Statistics Graphs, MCTs and Variability

Descriptive Statistics: Graphs, MCTs and Variability Sept 8th – 15th ____________________________________ 1) Demonstrate graphical methods for summarizing data a) Qualitative data. • Dot Diagrams • (Relative) Frequency tables • Bar graphs b) Quantitative data • Histograms • Stem-n-leaf diagrams 2) Discuss ethical issues related to presenting data graphically. 3) Present numerical methods for summarizing data including: a) Measures of central tendency • Mean • Median • Mode b) Measures of variability (spread) • Range • Inter-quartile Range • Variance • Standard Deviation Qualitative Data: What do I eat for Lunch? ___________________________________________ Mon Tues Wed Thurs Fri Sand ER Sand Salad Sand ER Sand Salad ER Pizza Sand Salad Pizza Salad Sand Pizza Sand Salad Sand Salad Salad Pizza Sand Pizza ER Sand Salad Pizza Sand Sand Key Definitions _____________________________________________ Class - • Not always easy Class Frequency – the number of observations Relative Class Frequency - the proportion of observations CF f n RCF = = = N n N Frequency Table ___________________________________________ Class Frequency Pizza 6 Salad 8 Sandwich 12 Egg Roll 4 ______________________________________________ x x x x x x x x x x x x x x Pizza Salad Dot Diagram x x x x x x x x x x x x Sandwich x x x x Egg Roll Relative Frequency vs. Frequency ___________________________________________ Class Frequency Relative Frequency (%) Pizza 6 Salad 8 Sandwich 12 Egg Roll 4 ______________________________________________ Healthy Lunch Choices? Freq (Rel Freq) 40 30 Freq 20 Rel Freq 10 0 Pizza Salad Sand Lunch Item ER Comparing Frequency and Relative Frequency ______________________________________________ Healthy Lunch Choices? 12 10 Freq 8 6 Freq 4 2 0 Pizza Salad Sand ER Lunch Item Healthy Lunch Choices? 40 Rel Freq 30 20 Rel Freq 10 0 Pizza Salad Sand Lunch Item ER Frequency Table ___________________________________________ Class Pizza Salad Sandwich Egg Roll Matt 6 8 12 4 Tammy 3 2 4 6 ___________________________________________ Who is healthier? 14 12 Freq 10 8 Matt 6 Tammy 4 2 0 Pizza Salad Sandwich Egg Roll Lunch Item Relative Frequency Table (%) ___________________________________________ Class Pizza Salad Sandwich Egg Roll Matt 20 26.7 40 13.3 Tammy ___________________________________________ Who is healthier? 40 Rel Freq 32 24 Matt 16 Tammy 8 0 Pizza Salad Sandwich Egg Roll Lunch Item Religious Affiliation Class Freq Rel Freq Amh Mont. Amh Mont. Buddhist 20 6 .01 .05 Catholic 376 15 .25 .13 Hindu 18 2 .01 .02 Jewish 175 25 .12 .21 Muslim 46 4 .03 .03 Protestant 852 65 .57 .56 Frequency Bar Graph ___________________________________________ 400 350 300 250 Freq 200 Amh 150 Mont 100 50 0 Budd Cath Hind Jew Mus Prot Religious Affiliation Relative Frequency Bar Graph 60.0 50.0 40.0 RF 30.0 Amh Mont 20.0 10.0 0.0 Budd Cath Hind Jew Mus Religous Affiliation Prot Plotting Quantitative Data ___________________________________________ 1) Categorizing the data Where do you place the boundaries for: a) High, middle low SES? b) Height? 2) Width of classes Equal is a good idea 3) Number of classes Take a good guess More data ===>more classes Plotting Quantitative Data ___________________________________________ Age of Memories for Older Adults Years Age Ago 0-10 60-70 Class Freq 149 Rel Freq .195 10-20 50-60 103 .134 20-30 40-50 75 .098 30-40 30-40 88 .114 40-50 20-30 134 .175 50-60 10-20 125 .163 60-70 0-10 92 .120 Real Stem and Leaf Diagram ___________________________________________ 10 0 0 9 0 0 2 3 6 6 6 8 9 9 9 8 0 0 1 1 2 2 3 4 4 5 5 6 6 6 7 8 8 9 9 9 7 0 0 1 3 3 3 5 6 6 6 7 7 7 7 8 8 8 9 6 0 0 1 3 3 6 7 8 9 9 9 5 1 3 4 4 5 5 8 8 Psych 22 Stem and Leaf Diagram ___________________________________________ 10 0 0 9 6 6 6 8 9 9 9 9 0 0 2 3 8 5 5 6 6 6 7 8 8 9 9 9 8 0 0 1 1 2 2 3 4 4 7 5 6 6 6 7 7 7 7 8 8 8 9 7 0 0 1 3 3 3 6 6 7 7 8 9 9 9 6 0 0 1 3 3 5 5 5 8 8 5 1 3 4 4 Exam Grade Histogram ______________________________________________ 20 18 16 14 12 Freq 10 8 6 4 2 0 100 90 80 70 Grade 60 50 Ethics and Graphs I ___________________________________________ Provide a scale 80.9 80.7 80.5 80.3 Males Females 80.1 79.9 79.7 79.5 Exam 1 Exam 2 81 80.5 Males Grade Females 80 79.5 Exam 1 Exam 2 Ethics and Graphs II ___________________________________________ Whenever possible, provide a zero point 90 80 70 60 Grade 50 Males 40 Females 30 20 10 0 Exam 1 Exam 2 Ethics and Graphs III ___________________________________________ Use equal-sized bins for your X-axis 30 25 20 Prem 15 10 5 0 1900-1950 1950-1980 1980-1995 1995-2000 Year 30 25 20 Prem 15 Series1 10 5 0 1910 1930 1950 Year 1970 1990 Words to Describe Distributions ___________________________________________ Uni-/Bi-Modal Refers to the number of Skewness Positively-Skewed Possessing a number of outliers at the EX: Income Time to run a mile Negatively-Skewed Distribution: Possessing a number of outliers at the EX: Exam scores Kurtosis Kind of a measure of Skewed Distributions ___________________________________________