Chapter 2 Homework Problems 1. Place the following set of n = 20 scores in a frequency distribution table. 6 2 2 1 3 2 4 7 1 2 5 3 1 6 2 6 3 3 7 2 3. Find each value requested for the distribution of scores in the following table. 𝑛= Σ𝑋 = Σ𝑋 2 Xf 5 2 4 3 3 5 2 1 1 1 5. For the following scores, the smallest value is X = 17 and the largest value is X = 52. Place the scores in a grouped frequency distribution table a) using an interval width of 5 points. b) using an interval width of 10 points. 44 19 23 17 25 47 32 26 25 30 18 24 49 51 24 19 43 27 34 18 52 18 36 25 7. For each of the following samples, determine the interval width that is most appropriate for a grouped frequency distribution and identify the approximate number of intervals needed to cover the range of scores. a. Sample scores range from X = 8 to X = 41. b. Sample scores range from X = 16 to X = 33. c. Sample scores range from X = 26 to X = 98. 9. Describe the difference in appearance between a bar graph and a histogram and identify the circumstances in which each type of graph is used. 1 11. Sketch a histogram and a polygon showing the distribution of scores presented in the following table: Xf 7 1 6 1 5 3 4 6 3 4 2 1 13. A survey given to a sample of college students contained questions about the following variables. For each variable, identify the kind of graph that should be used to display the distribution of scores (histogram, polygon, or bar graph). a. b. c. d. number of brothers and sisters birth-order position among siblings (oldest = 1st) gender (male/female) favorite television show during the previous year 15. Gaucher, Friesen, and Kay (2011) found that masculine-themed words (such as competitive, independent, analyze, strong) are commonly used in job recruitment materials, especially for job advertisements in male-dominated areas. In a similar study, a researcher counted the number of masculine-themed words in job advertisements for job areas, and obtained the following data. Area Number of Masculine Words Plumber 14 Electrician 12 Security guard 17 Bookkeeper 9 Nurse 6 Early-Childhood Educator 7 Determine what kind of graph would be appropriate for showing this distribution and sketch the frequency distribution graph. 2 17. For the following set of scores: 5 8 5 7 6 6 5 7 4 6 6 9 5 5 4 6 7 5 7 5 a) Place the scores in a frequency distribution table. b) Identify the shape of the distribution. 19. For the following set of scores: 8 6 7 5 4 10 8 9 5 7 2 9 9 10 7 8 8 7 4 6 3 8 9 6 a. Construct a frequency distribution table. b. Sketch a histogram showing the distribution. c. Describe the distribution using the following characteristics: 1) What is the shape of the distribution? 2) What score best identifies the center (average) for the distribution? 3) Are the scores clustered together, or are they spread across the scale? 21. Recent research suggests that the amount of time that parents spend talking about numbers can have a big effect on the mathematical development of their children (Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010). In the study, the researchers visited the children’s homes between the ages of 14 and 30 months and recorded the amount of “number talk” they heard from the children’s parents. The researchers then tested the children’s knowledge of the meaning of numbers at 46 months. The following data are similar to the results obtained in the study. Children’s Knowledge-of-Numbers Scores for Two Groups of Parents Low Number-Talk Parents High Number-Talk Parents 2, 1, 2, 3, 4 3, 4, 5, 4, 5 3, 3, 2, 2, 1 4, 2, 3, 5, 4 5, 3, 4, 1, 2 5, 3, 4, 5, 4 Sketch a polygon showing the frequency distribution for children with low number-talk parents. In the same graph, sketch a polygon showing the scores for the children with high number-talk parents. (Use two different colors or use a solid line for one polygon and a dashed line for the other.) Does it appear that there is a difference between the two groups? 3 Scanned with CamScanner Scanned with CamScanner Scanned with CamScanner
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