Chapter 6: Descriptive Statistics
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1 Chapter 6: Descriptive Statistics Problem (01): Make a frequency distribution table for the following data using 5 classes Problem (02): Annual Salaries Sample (in thousands of dollars) for municipal employees in Los Angeles and Long Beach are listed. Los Angeles Long Beach Find the number of classes and the class range, variance, and standard deviation of each data set. Engr. Yasser M. Almadhoun Page 1
2 9 = 3 n = = (X 2 Variance (S 2 X ) ) = n 1 = = (X X ) 2 Standard deviation (S) = n 1 = = = = 3 n = = (X 2 Variance (S 2 X ) ) = n 1 = = Standard deviation (S) = (X X ) 2 n 1 Engr. Yasser M. Almadhoun Page 2
3 = = = 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 n = = Engr. Yasser M. Almadhoun Page 3
4 Lower Least quartile Median Upper quartile Greatest Interquartile range Mean Problem (04): The data set is the number of minutes a sample of 25 people exercise each week (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
5 Engr. Yasser M. Almadhoun Page 5
6 n = = Lower Least quartile Median Upper quartile Greatest Interquartile range Mean Engr. Yasser M. Almadhoun Page 6
7 Problem (05): The number of wins for each Major-League Baseball team in 2003 are listed (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
8 n = = Lower Least quartile 43.0 Median Upper quartile Greatest Interquartile range Mean Problem (06): For the following set of data, using five classes, find: (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
9 n = 36 = 6 Engr. Yasser M. Almadhoun Page 9
10 Problem (07): The grades of 20 students in statistics midterm exam are as follow: (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 = = Engr. Yasser M. Almadhoun Page 10
11 Trimmed mean (X ) T10% = X n = = X (X X ) (X X ) 2 (X 2 Variance (S 2 X ) ) = n 1 = = Standard deviation (S) = (X X ) 2 n 1 Engr. Yasser M. Almadhoun Page 11
12 = = = 6.24 n = = Engr. Yasser M. Almadhoun Page 12
13 Lower Smaller quartile 10.0 Median Upper quartile Greatest Interquartile range 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 (d) One half of the cholesterol levels are between 180 and 211. Engr. Yasser M. Almadhoun Page 13
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