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Homework • Line of best fit page 1 and 2 Displaying and Describing Categorical & Quantitative Data You should be able to: • Recognize when a variable is categorical or quantitative • Choose an appropriate display for a categorical variable and a quantitative variable • Summarize the distribution with stem-leaf plot, histogram, dot plot, box plots • Be able to describe the distribution of quantitative variables in terms of its shape, center, spread, and outliers. Types of Graphs • • • • Histogram Dot plot Stem leaf plot Boxplots Variables Come in 2 Varieties 1. Categorical (or Qualitative) 2. Quantitative (or Numerical) 1. 2. Discrete Continuous Introduction to Statistics-Variables 5 Categorical Data • The objects being studied are grouped into categories based on some qualitative trait. • Example: eye color, type of car you drive, gender, etc. Categorical Data (Single Variable) Eye Color BLUE BROWN GREEN Frequency (COUNTS) 20 50 5 Relative Frequency 20/75 = 0.27=27% 50/75= 0.66=66% 5/75= 0.07=7% Quantitative Variables • Variables that are numerical. They represent a measurable quantity. – Discrete: values that are only be whole numbers – Continuous: values that can be in decimals. • Example: person’s height, # of hamburgers sold each day of the week, speed of a car, pulse rate, etc Discrete vs Continuous data Determine which one is a discrete and continuous data http://www.shmoop.com/probability-statistics/discrete-continuous-data-exercises.html Go to kahoot.it Dot Plot • Summarizes quantitative data. • Horizontal axis represents measurement scale. • Plot one dot for each data point. Dot Plot Fastest Ever Driving Speed 226 Stat 100 Students, Fall '98 100 Men 126 Women 70 80 90 100 110 120 130 140 150 160 Speed Stem-and-Leaf Plot • Summarizes quantitative data • Each data point is broken down into a “stem” and a “leaf.” • First, “stems” are aligned in a column. • Then, “leaves” are attached to the stems. Period 2: 57 60 88 85 79 70 65 98 97 59 58 65 62 77 77 75 73 69 82 81 Stem 5 Key: 7 9 means 79 Leaf 7 8 9 6 0 2 5 5 9 7 0 3 5 7 7 9 8 9 1 2 5 8 7 8 Histogram • Summarizes quantitative data • Divide measurement up into equal-sized categories (BIN WIDTH) • Determine number (or percentage) of measurements falling into each category. • Draw a bar for each category so bars’ heights represent number (or percent) falling into the categories. • Label and title appropriately. Histogram Age of Spring 1998 Stat 250 Students 50 40 30 20 10 0 18 19 20 21 22 23 24 Age (in years) n=92 students 25 26 27 Strengths and Weaknesses of Graphs for Quantitative Data • Histograms – Uses intervals – Good to judge the “shape” of a data – Not good for small data sets • Stem-Leaf Plots – Good for sorting data (find the median) – Not good for large data sets Strengths and Weaknesses of Graphs for Quantitative Data • Dotplots – Uses individual data points – Good to show general descriptions of center and variation – Not good for judging shape for large data sets Finding Individuals & Variables in a List State Region Population Males Females Alabama Alaska South West 15.6m 5.4m 8.3m 2.5m 7.2m 2.9m Arizona West 10.2m 5.1m 5.1m Individuals in Sample—Usually in 1st Column Variables—Usually in 2nd and succeeding columns Number of in Sample = 3 Who’s in Sample? Alabama, Alaska, Arizona Variable = Region = Categorical Variable = Population = Discrete Quantitative Variable = Males = Discrete Quantitative Variable = Females = Discrete Quantitative Look for Variable Names in Column Headings Introduction to Statistics-Variables 18 Categorical or Quantitative If Categorical, one possible category? If Quantitative, Continuous or Discrete? 1) 2) 3) 4) 5) 6) Length of a pen? Type of pen? Number of pens in box? Maker of pen? Flow of ink in ml/sec? Color of pen’s ink? Quantitative, Continuous Categorical Quantitative, Discrete Categorical Quantitative, Continuous Categorical Introduction to Statistics-Variables 19 Categorical or Quantitative If Categorical, one possible category? If Quantitative, Continuous or Discrete? Subject of a book? Number of pages in the book? Quantitative, Discrete Area of each page of book? Number of letters on a page? Number of weeks on best seller list? Categorical Quantitative, Continuous Quantitative, Discrete Quantitative, Discrete Introduction to Statistics-Variables 20 Categorical or Quantitative If Categorical, one possible category? If Quantitative, Continuous or Discrete? 1) 2) 3) 4) 5) 6) 7) Style of pants? Color of pants? Number of pairs of pants you own? # of pockets on pants? Size of pants? Maker of the pants? Length of inseam on the pants? Introduction to Statistics-Variables Categorical Categorical Quantitative, Discrete __________________ categorical Categorical Quantitative, Continuous 21