Chapter 6: Descriptive Statistics Problem (01): Make a frequency distribution table for the following data using 5 classes. 5 10 7 19 25 12 15 7 6 8 17 17 22 21 7 7 24 5 6 5 Problem (02): Annual Salaries Sample (in thousands of dollars) for municipal employees in Los Angeles and Long Beach are listed. Los Angeles 20.2 26.1 20.9 32.1 35.9 23 28.2 31.6 18.3 Long Beach 20.9 18.2 20.8 21.1 26.5 26.9 24.2 25.1 22.2 Find the number of classes and the class range, variance, and standard deviation of each data set. Engr. Yasser M. Almadhoun Page 1
9 = 3 n = 236.3 = 26.26 9 (X 2 Variance (S 2 X ) ) = n 1 = 360.8241 9 1 = 45.10 (X X ) 2 Standard deviation (S) = n 1 = 360.8241 9 1 = 45.10 = 6.72 9 = 3 n = 205.9 = 22.88 9 (X 2 Variance (S 2 X ) ) = n 1 = 116.8209 9 1 = 14.60 Standard deviation (S) = (X X ) 2 n 1 Engr. Yasser M. Almadhoun Page 2
= 116.8209 9 1 = 14.60 = 3.82 Problem (03): The weights (in pounds) of the defensive players on a high school football team are given. (a) Make a boxplot of the data. (b) Find the mode. 173 145 205 192 197 227 156 240 172 185 208 185 190 167 212 228 190 184 195 n = 3651 19 = 192.16 Engr. Yasser M. Almadhoun Page 3
Lower Least quartile 145.0 Median Upper quartile 173.0 190.0 208.0 Greatest 240.0 35.0 Interquartile range 192.16 Mean Problem (04): The data set is the number of minutes a sample of 25 people exercise each week. 108 139 120 123 120 132 123 131 131 157 150 124 111 101 135 119 116 117 127 128 139 119 118 114 127 (a) Make a frequency distribution of the data set using five classes. Include class limits, midpoints, frequencies, boundaries, relative frequencies, and cumulative frequencies. (b) Display the data using a frequency histogram and a frequency polygon on the same axes. (c) Display the data using a relative frequency histogram. (d) Display the data using a boxplot. (e) Display the data using an ogive Engr. Yasser M. Almadhoun Page 4
Engr. Yasser M. Almadhoun Page 5
n = 3129 25 = 125. 16 Lower Least quartile 101.0 Median Upper quartile 117.5 123.0 131.5 Greatest 157.0 14.0 Interquartile range 125.16 Mean Engr. Yasser M. Almadhoun Page 6
Problem (05): The number of wins for each Major-League Baseball team in 2003 are listed. 101 95 86 71 63 90 86 83 68 43 96 93 77 71 101 91 86 83 66 88 87 85 75 69 68 100 85 84 74 64 (a) Find the quartiles of the data set. (b) Find the interquartile range. (c) Draw a boxplot. (d) Find the mode. Engr. Yasser M. Almadhoun Page 7
n = 2429 30 = 80.97 Lower Least quartile 43.0 Median Upper quartile 71.75 84.5 90.0 Greatest 101.0 19.0 Interquartile range 80.97 Mean Problem (06): For the following set of data, using five classes, find: 87 82 64 95 66 75 88 92 67 77 71 76 93 88 75 55 69 87 61 94 87 74 66 92 69 77 92 83 85 90 65 74 84 65 91 70 (a) The frequency distribution table. (b) The relative frequency distribution table. (c) The Frequency Histogram. (d) Present the data as stem-and-leaf plot. Engr. Yasser M. Almadhoun Page 8
n = 36 = 6 Engr. Yasser M. Almadhoun Page 9
Problem (07): The grades of 20 students in statistics midterm exam are as follow: 30 21 15 14 10 19 14 22 27 30 20 18 23 15 16 16 15 29 28 13 (a) Calculate the sample mean and the trimmed mean. (b) Calculate the sample standard deviation. (c) Find the quartiles. (d) Draw a boxplot of the above data set. (Question 6: in Final Exam 2005) n = 395 20 = 19.75 Engr. Yasser M. Almadhoun Page 10
Trimmed mean (X ) T10% = X n = 312 16 = 19.50 X (X X ) (X X ) 2 (X 2 Variance (S 2 X ) ) = n 1 = 739.75 20 1 = 38.93 Standard deviation (S) = (X X ) 2 n 1 Engr. Yasser M. Almadhoun Page 11
= 739.75 20 1 = 38.93 = 6.24 n = 395 20 = 19.75 Engr. Yasser M. Almadhoun Page 12
Lower Smaller quartile 10.0 Median Upper quartile 15.0 18.5 26.0 Greatest 30.0 11.0 Interquartile range 19.75 Mean Problem (08): Use the boxplot below to determine which statement is accurate (choose the best alternative): (a) About 25% of the adults have cholesterol levels of at most 211. (b) About 75% of the adults have cholesterol levels less than 180. (c) One half of the cholesterol levels are between 180 and 197.5. (d) One half of the cholesterol levels are between 180 and 211. Engr. Yasser M. Almadhoun Page 13