Stats 201 Ch 1

1. Place the following sample of n = 20 scores in a frequency distribution table. 6, 9, 9, 10, 8, 9, 4, 7, 10, 9 5, 8, 10, 6, 9, 6, 8, 8, 7, 9

1. X f ──── 10 3 9 6 8 4 7 2 6 3 5 1 4 1 ────

10. For the following set of quiz scores: 3, 5, 4, 6, 2, 3, 4, 1, 4, 3 7, 7, 3, 4, 5, 8, 2, 4, 7, 10 a. Construct a frequency distribution table to organize the scores. b. Draw a frequency distribution histogram for these data

10. a. X f 10 1 9 0 8 1 7 3 6 1 5 2 4 5 3 4 2 2 1 1

12. A survey given to a sample of 200 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. number of pizzas consumed during the previous week b. size of T-shirt worn (S, M, L, XL) c. gender (male/female) d. grade point average for the previous semester e. college class (freshman, sophomore, junior, senior)

12. a. histogram or polygon (ratio scale) b. bar graph (ordinal scale) c. bar graph (nominal scale) d. histogram or polygon (ratio scale) e. bar graph (ordinal scale)

15. For the following set of scores Scores: 5, 6,8, 9,5,5,7,5,6,4,6,6,5,7,7,5,4,7,6, 5 a. Place the scores in a frequency distribution table. b. Identify the shape of the distribution.

15. a. ──── X f ──── 9 1 8 1 7 4 6 5 5 7 4 2 ──── b. positively skewed

16. Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of the distribution? 5, 6, 4, 7, 7, 6, 8, 2, 5, 6 3, 1, 7, 4, 6, 8, 2, 6, 5, 7

16. ──── X f ──── 8 2 7 4 . 6 5 5 3 4 2 3 1 2 2 1 1 ──── Negatively skewed

3. Find each value requested for the distribution of scores in the following table. a.n b.EX c. EX^2 x f 5 2 4 3 3 5 2 1 1 1

3. a. n = 12 b. ΣX = 40 c. ΣX2 = 148

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 = 24 to X = 41 b. Sample scores range from X = 46 to X = 103 c. Sample scores range from X = 46 to X = 133

7. a. 2 points wide and around 8 intervals b. 5 points wide and around 12 intervals or 10 points wide and around 6 intervals c. 10 points wide and around 9 intervals

8. What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped table?

8. A regular table reports the exact frequency for each category on the scale of measurement. After the categories have been grouped into class intervals, the table reports only the overall frequency for the interval but does not indicate how many scores are in each of the individual categories.

9. Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in which each type of graph is used.

9. A bar graph leaves a space between adjacent bars and is used with data from nominal or ordinal scales. In a histogram, adjacent bars touch at the real limits. Histograms are used to display data from interval or ratio scales.

25. Construct a stem and leaf display for the data in problem 6 using one stem for the scores in the 60s, one for scores in the 50s, and so on.

25. 1│796 2│0841292035826 3│094862 4│543 5│3681 6│4

2. Construct a frequency distribution table for the following set of scores. Include columns for proportion and percentage in your table.

2. X f p % ──────────── 9 2 0.10 10% 8 3 0.15 15% 7 5 0.25 25% 6 4 0.20 20% 5 3 0.15 15% 4 2 0.10 10% 3 1 0.05 5% ────────────

22. Find the requested percentiles and percentile ranks for the following distribution of quiz scores for a class of N = 40 students. X f cf c% 20 2 40 100.0 19 4 38 95.0 18 6 34 85.0 17 13 28 70.0 16 6 15 37.5 15 4 9 22.5 14 3 5 12.5 13 2 2 5.0 a. What is the percentile rank for X = 15? b. What is the percentile rank for X = 18? c. What is the 15th percentile? d. What is the 90th percentile?

22. a. The percentile rank for X = 15 is 17.5%. b. The percentile rank for X = 18 is 77.5%. c. The 15th percentile is X = 14.75. d. The 90th percentile is X = 19.

23. Use interpolation to find the requested percentiles and percentile ranks requested for the following distribution of scores. X f fc f c% 14-15 3 50 100 12-13 6 47 94 10-11 8 41 82 8-9 18 33 66 6-7 10 15 30 4-5 4 5 10 2-3 1 1 2 a. What is the percentile rank for X = 5? b. What is the percentile rank for X = 12? c. What is the 25th percentile? d. What is the 70th percentile?

23. a. The percentile rank for X = 5 is 8%. b. The percentile rank for X = 12 is 85%. c. The 25th percentile is X = 7. d. The 70th percentile is X = 10.

24. The following frequency distribution presents a set of exam scores for a class of N = 20 students. X f cf c% 90-99 4 20 100 80-89 7 16 80 70-79 4 9 45 60-69 3 5 25 50-59 2 2 10 a. Find the 30th percentile. b. Find the 88th percentile. c. What is the percentile rank for X = 77? d. What is the percentile rank for X = 90?

24. a. The 30th percentile is X = 72. b. The 88th percentile is X = 93.5. c. The percentile rank for X = 77 is 40%. d. The percentile rank for X = 90 is 81%.

27. Use a stem and leaf display to organize the following distribution of scores. Use seven stems with each stem corresponding to a 10-point interval. Scores: 28, 54, 65, 53, 81 45, 44, 51, 72, 34 43, 59, 65, 39, 20 53, 74, 24, 30, 49 36, 58, 60, 27, 47 22, 52, 46, 39, 65 hj

Ni j2b n997. 2 │80472 3 │49069 4 │543976 5 │4319382 6 │5505 7 │24 8 │1

26. A set of scores has been organized into the following stem and leaf display. For this set of scores: a. How many scores are in the 70s? b. Identify the individual scores in the 70s. c. How many scores are in the 40s? d. Identify the individual scores in the 40s. 3 8 4 60 5 734 6 81469 7 2184 8 247

Thanks so that the only thing26. a. 4 b. 72, 71, 78, and 74 c. 2 d. 46 and 40

4. Find each value requested for the distribution of scores in the following table. a. n b. EX c. Ex^2 Frequency table X: 5 4 3 2 1 f: 1 2 3 5 3

a. n=14 b. EX = 35 c. 107