# ch02 - Chapter Two 2.1 Data in their original form are...

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Chapter Two 2.1 Data in their original form are usually too large and unmanageable. By grouping data, we make them manageable. It is easier to make decisions and draw conclusions using grouped data than ungrouped data. 2.3 a. & b. Category Frequency Relative Frequency Percentage A 8 .267 26.7 B 8 .267 26.7 C 14 .467 46.7 c. 26.7 % of the elements in this sample belong to category B. d. 26.7% + 46.7% = 73.4% of the elements in this sample belong to category A or C. e. 0 4 8 12 16 A B C Category Frequency 2.5 a. & b. Category Frequency Relative Frequency Percentage F 12 .24 24 SO 12 .24 24 J 15 .30 30 SE 11 .22 22 c. 30 + 22 = 52% of the students are juniors or seniors. d. 0 4 8 12 16 F SO J SE Category Frequency 2.7 a. & b. Category Frequency Relative Frequency Percentage C 9 9/20= .45 45 9

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10 F 5 5/20= .25 25 T 6 6/20= .30 30 c. 45% of the employees would prefer a four-day work week. d. T 30% F 25% C 45% 2.9 Let the seven categories listed in the table be denoted by S, HC, R, O, E, P, and U respectively. E 12% P 3% S 26% O 12% R 19% HC 20% U 8% 2.11 1. The number of classes to be used to group the given data. 2. The width of each class. 3. The lower limit of the first class. 2.13 A data set that does not contain fractional values is usually grouped by using classes with limits. Suppose we have data on ages of 100 managers, and ages are rounded to years. Then, the following table could be an example of grouped data that uses classes with limits. Ages (years) Frequency 21 to 30 12 31 to 40 27 41 to 50 31 51 to 60 22 61 to 70 8 A data set that contains fractional values is grouped by using the less than method. Suppose we have data on sales of 100 medium sized companies. The following table shows a frequency table for such data. Sales(millions of dollars) Frequency 0 to less than 10 27 10 to less than 20 31
Mann - Introductory Statistics , Fifth Edition, Students Solutions Manual 20 to less than 30 19 30 to less than 40 14 40 to less than 50 9 Single valued classes are used to group a data set that contains only a few distinct values. As an example, suppose we have a data set on the number of children for 100 families. The following table is an example of a frequency table using single valued classes. Number of Children Frequency 0 13 1 26 2 38 3 18 4 5 2.15 a. & c. Class Boundaries Class Midpoint Relative Frequency Percentage 17.5 to less than 30.5 24 .24 24 30.5 to less than 43.5 37 .38 38 43.5 to less than 56.5 50 .28 28 56.5 to less than 69.5 63 .10 10 Note: To calculate Relative Frequency and Percentage for quantitative data when using technology simply follow the procedures for qualitative data outlined in section 2.2 of the text or in problem 2.3. b. Yes, each class has a width of 13. d. 24 + 38 = 62% of the employees are 43 years old or younger. 2.17 a., b., & c. Class Limits Class Boundaries Class Width Class Midpoint 1 to 25 .5 to less than 25.5 25 13 26 to 50 25.5 to less than 50.5 25 38 51 to 75 50.5 to less than 75.5 25 63 76 to 100 75.5 to less than 100.5 25 88 101 to 125 100.5 to less than 125.5 25 113 126 to 150 125.5 to less than 150.5 25 138 2.19 a. & b.

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