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1-26 - Chapter 1 Exploring Data Using the results from...

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Unformatted text preview: Chapter 1 - Exploring Data Using the results from Examples 1 and 2, answer the following questions a. What is the range of the data? Does there appear to be any outliers? Fanaal too — 72: 28 outliers: Nyélrn'rifi key/E. V b. Does the distribution contain one or more gaps? Are there clusters? Sq? 5‘. Perhaps 5:014 Hones - — Prabq bl): if? 5 fear! {firm '5 -Clu5&(§3 bebably '0- around! ‘(S i: 85. c. Is the distribution of the exam scores symmetric? Or is it skewed? 51 ibh'clf 5 Feweok la‘p‘b . Skewed Right Symmetric Skewed Left kA Example 8: Babe Ruth vs. Hank Aaron (Section 1.2, Exercise #3, p.23) The number of home runs hit by Babe Ruth during his 15 years with the Yankees, from 1920 to 1934, are as follows: 54 59 35 41' 46 25 47 60 54 46 49 46 41 34 22 The number of home runs hit by Hank Aaron during his 21 years with the Braves are as follows: E 13 '27 26 44 3O 39 4O 34 45 44 24 32 44 39 . 29 44 38 47 34 4O 20 M Construct a back-to-back stem-and-leaf plot comparing Ruth and Aaron. , 13. EZZOHG7‘1 5H502HL‘8C‘C‘ q7®Cp®llHOOHHHH57 L1 5 ‘1 23¢ 9 . Ruth , Aaron Chapter 1 — Exploring Data 1.3 Graphing Categorical Data Dotplots and stem-and-leaf plots are ways of organizing data and are part of the modern approach to descriptive statistics called exploratory data analysis (EDA). These tools are useful, but they are not recommended for categorical variables since the categories do not have order. One graphical tobl for categorical variables is a frequency table where the number, or frequency, of subjects. per category is listed. Bar graphs arethen constructed to display the information in the frequency table. When the rectangles in the bar chart are displayed from tallest to shortest, the chart is called a Pareto chart. Example 9: Favorite Colors Forty randomly chosen customers at an office supplies store were asked to state the color of pen that they like the most. The preferences are listed below. (R = red, G = green, B = blue, P = purple, K = Black) RKBPGRBKKRBKGRKKKRPK RGRKVRBGRPBKGRBKBGGBP a) Create a frequency table and a bar chart for the data. 10 % fl . Q Chapter 1 - ExplorIng Data 68 135 . g b) Create a Pareto chart for the data. Q I5 e E e ? Q1. Q ; Q Q ' Q If we are interested in the percentage of total subjects in each category, rather than 1,; Q the frequencies, a pie chart should be used instead. Q Example 10: Daily Schedule E Q The following table gives the breakdown of a day in the life of a typical college student. Q Use the data to construct a pie chart. g . - Activity Number of Hours ‘ 7., X 390') __.__o E Q Sleep . 8 335% \20 "‘r Class . 3 l 2. 5% “l 5° Studying/Homework 2.5 lb Hf]; ”7° "1: '1. 6° E Meals 2 8. 3 7o ’50 o Job 5 20. a? ‘70 7 5° ‘ Miscellaneous . H. 593 °7o 11 bobbcccabcaeaoeabab Chapter 1 — Exploring Data 1.4 Frequency Histograms Example 11: Final Exam Grades Given below are final exam grades from a basic statistics course. Draw a frequency histogram based 6n the data. M 75 87 51 64 60 83 65 63 50 74 89 97 63 83 76 98 75 62 84 92 86 73 80 88 9O 70 85 92 96 79 m Step 1. Divide the range of the data into class intervals of equal width Step 2. Count the number of observations in each class interval Step 3. Draw the histogram 12 Chapter 1 — Exploring Data To focus on the overall shape of the distribution and ignore the minor irregularities, a smooth curve is sometimes superimposed on the histogram. l l ' ‘ l Example 12: Distribution Shapes l Match the following types of distribution shapes to their appropriate distributions. 9 D Shape A D - ' . D E Bell-Shaped Q r s , . ,2! . 9 Shape B Q . 9 ___D_____ Left-Skewed Q Q Q ‘ ' Shape C 3 A Right—Skewed Q Q 9 Shape D Q Q B Uniform , Q Q Q 9 Shape E Q ___Q__ U—Shaped ’ . '13 Chapter 1 — Exploring Data , 1.5 Density Histograms When the areas of the rectangles in the histogram add to 100%, the resulting figure is a density histogram, where the height of each rectangle represents the density, or m '2 crowdedness, of that interval. ‘ ' ' For discrete variables, or counting variables, the rectangles are centered over the . , . values they take. 50 if the variable has values 0, 1, 2, 3, ..., the class intervals are -0.5 ' -.~ 6 to 0.5, 0.5 to 1.5, 1.5 to 2.5, 2.5 to 3.5, and so on. -. _§ Example 13: Final Exam Grades, revisited Given below are final exam grades from a basic statistics course, previously given in ’ 2 Example 11. Draw a frequency histogram based on the data. After drawing the ~. frequency histogram, answer the questions that follow. W 75 87 51 64 6O 83 65 63 50 74 89 97 63 83 76 98 75 62 84 92 86 73 80 88 90 70 85 92 96 79 [fifififififlfififififififi@fififififififififififififififi%fifififififififié%@%%% - Chapter 1 _, Exploring Data a) How does the density histogram compare with the histogram drawn for Example 11? b) What is the shape of this density histogram? §\ {El/THY lap-é — skewed c) What is the approximate percentage of people who made an 80? 55b cl) What is the approximate percentage of people who made at least a 70, but rat mane than an 80? ' lest; .— e) What is the approximate percentage of people who made at least a 90? 20(2); f)' What is the approximate percentage of people who made at most a 70? (0.2;?) + 2090 + 2.3720 : 2:190 9) Which interval has the largest area? Bo—qa“ h) Which interval is the most dense? 80—90“ 15 ...
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