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Unformatted text preview: Posted before class WEEK 9 Mon, Oct 25 GRAPHICAL DISPLAYS (Background material is in Chapter 1) Numerical Data Distributions Shapes of Distributions (Chap 1, Sec 5) Discuss Skewness only, not Kurtosis. Delay discussion until after we have covered graphical displays in Section 9. Numerical Data Distributions Graphical Displays (Chap 1, Sec 9) Example 1. Numerical variable named C3 (n = 26) . C3 23 18 16 26 9 27 10 19 15 22 24 14 15 26 25 17 16 14 24 25 7 25 20 22 24 23 1 C3 StemandLeaf Displays n = 26 Stem Leaf We see Median = 21 0 0 097 079 1044 1044 18695576 15566789 232440243 202233444 2676555 2555667 Minitab Software was used for the calculations and displays below. Variable n Mean StDev Min Q1 Median Q3 Max C3 26 19.46 5.73 7.00 15.00 21.00 24.25 27.00 Dotplot of C3 27 24 21 18 15 12 9 C3 Dotplot of C3 2 Histogram of C3 25 20 15 10 9 8 7 6 5 4 3 2 1 C3 Frequency Histogram of C3 Box Plot of C3 The box plot reveals that the data are skewedtothe left (which can be stated skewedtowardthe smallvalues ). 30 25 20 15 10 C3 Boxplot of C3 3 Example 2. Consider the same data as shown above but with score 7 replaced by 1 . Variable n Mean StDev Min Q1 Median Q3 Max C5 26 19.23 6.34 1.00 15.00 21.00 24.25 27.00 30 25 20 15 10 5 C5 Boxplot of C5 Skewed to the left. 4 Example 3. x = No. Correct out of 30 on Exam 1 (n = 604) . Variable n Mean StDev Min Q1 Median Q3 Max x 604 21.199 4.678 5.000 18.000 22.000 25.000 30.000 30 25 20 15 10 5 x Boxplot of x Skewed to the left. 28 24 20 16 12 8 4 x Dotplot of x Each symbol represents up to 2 observations. 5 28 24 20 16 12 8 70 60 50 40 30 20 10 x Frequency Histogram of x Note. One should investigate outliers in an attempt to find reasons for the extremeness. Sometimes simple errors in recording data explain the extremeness. In the case of the score x = 5, the exam was scored by the wrong key. When scored with the correct key, the score for the student was found to be x = 18. 6 Exercise 118 . Discuss Exercise 135 . You may use the fact that 3197 16 1 = = i i x and 2291949 16 1 2 = = i i x EXER 148 (n+1)P x x sorted Position P Position Quartiles 7.0 5.5 1 0.25 8.75 6.525 Q1 6.9 5.6 2 0.50 17.5 7.2 Q2 8.2 5.8 3 0.75 26.25 7.6 Q3 7.8 5.8 4 7.7 6.0 5 7.3 6.1 6 6.8 6.2 7 6.7 6.3 8 8.2 6.6 9 8.4 6.7 10 7.0 6.7 11 6.7 6.7 12 7.5 6.8 13 7.2 6.9 14 7.9 7.0 15 7.6 7.0 16 6.7 7.2 17 6.6 7.2 18 6.3 7.2 19 5.6 7.3 20 7.8 7.3 21 5.5 7.3 22 6.2 7.4 23 5.8 7.5 24 5.8 7.5 25 6.1 7.6 26 6.0 7.6 27 7.3 7.7 28 7.3 7.8 29 7.5 7.8 30 7.2 7.9 31 7.2 8.2 32 7.4 8.2 33 7.6 8.4 34 Some additional comments in regard to Graphical Displays.Some additional comments in regard to Graphical Displays....
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 Spring '08
 Anderson

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