5 or an 8. How many intervals should your scale have?3 If you wanted to determine how many scores were in a data set, which frequency table column would provide this information most efficiently?
4 What does a relative frequency tell you?
5 You are checking the grade of your last English test and notice that your professor provided you with a cumulative relative frequency table as well. You notice that cumulative relative frequency of your score was .34. What does this mean?
6 When should you consider making a grouped frequency table as opposed to a regular frequency table?
7 What is a percentile rank?
Answers
1 The data are organized in an efficient manner such that you can easily determine how many of any particular score are in the data set. When viewing raw scores, especially those out of order, it can be difficult to determine this information.
2 It should still have 10 intervals.
3 The cumulative frequency column.
4 The proportion of the sample that obtained a particular score.
5 34% of the class scored the same or lower than you and 66% of the class scored higher.
6 There is no standard rule for creating a grouped frequency table. However, you should consider using this when the scale for your data set is so large that it would be cumbersome to use a standard frequency table.
7 A percentile rank is the percentage or proportion of cases falling at or below a specific score.
Multiple-Choice Questions
The following scores represent the amount of fear (scored on a scale of 1–15) experienced when going through a haunted house on Halloween. Use the following table for Questions 1 to 6.
1 What is the cumulative frequency (starting from the bottom) at a fear of 5?217293103
2 How many people visited the haunted house this past Halloween?12321315120
3 What is the approximate relative frequency of people that provided a rating of 10?0.070.700.050.50
4 What is the cumulative relative frequency (starting from the bottom) of a rating of 15?0.100.40.981.0
5 If you were to draw a relative frequency curve of these data, how would you describe the shape of this distribution?SymmetricalPositively skewedNegatively skewedBimodal
6 What is the cumulative relative frequency (starting from the bottom) of a score of 11?27.45%88.73%94.31%74.85%
7 In a study of posttraumatic stress, you obtain ratings of the number of flashbacks a person has in a month. If you have a sample of 81 individuals, and 23 have indicated they have had flashbacks twice in the past month, what is the relative frequency of those with two flashbacks in the past month?0.630.400.280.53
Multiple-Choice Answers
1 C
2 B
3 A
4 D
5 B
6 B
7 C
Module Quiz
1 Using the following data, create a frequency table, cumulative frequency table, and relative frequency table.7 8 410 6 45 7 73 5 64 3 9
2 You are investigating a measure of well-being in a geriatric population. The scale has a range of 0 to 50. The cumulative relative frequency for a score of 44 is 34% and the relative frequency is 4% for that interval. Why is the percentile rank of those with a score of 44 equal to 32% and not 34%?
3 You had a percentile rank of 86 in your high school class. What percentage of students were ranked above you?
4 You are trying to arrange the SAT scores of your high school in a frequency table. You realize that you need to use a grouped frequency table because of the large scale (0–1,600), so you decide to create intervals of 400. Was this a good idea?
5 Name a variable that you think would have (a) a negative distribution, (b) a positive distribution, (c) a bimodal distribution, (d) a normal distribution.
Quiz Answers
1
2 Percentile ranks are based on the real limits of a score. The cumulative relative frequency was 34% with a relative frequency of 4%, indicating that 30% of the scores were below this interval and 4% of the scores above this interval. Also, you can assume that the scores were evenly distributed within this interval. Thus, you have to add the amount of scores below (30%) to 1/2 of the amount of scores within it (4%), or 2%. This provides you with a percentile rank of 32%.
3 14%.
4 This was probably not a good idea. You would have 4 groups, and you would expect not many people to fall in the lowest group. Also, you would lose a great deal of precision, as most people would score between 800 and 1,200, which would be just one interval.
5 Answers will vary.
Module 4 Graphs and Plots
Learning Objectives
Determine the utility of using graphs to represent data
Determine methods to graph continuous data
Identify symmetry, skew, and kurtosis in a distribution
Determine methods to graph discrete data
Module Summary
Although frequency tables provide a neat method for organizing data, graphs can be an even more effective method for presenting information. Information that can be obtained from a graph includes the dispersion, clustering, and location of the majority of scores.
When creating a graph, the traditional rules are that the X-axis (abscissa) represents the intervals of the measured variable and the Y-axis (ordinate) represents the frequency of scores at each interval. In situations where there is a large frequency of cases for a particular score interval, you can divide the interval on the X-axis.
There are some rules for creating a graph, which are as follows: (1) The Y-axis should be 3/4 the size of the X-axis. (2) With large data sets, you can collapse intervals on the X-axis so that there are at least 5 intervals but not more than 12 intervals. (3) Each interval on the X-axis must be equal to the others. (4) The Y-axis must be continuous. (5) The axes should not stretch or compress the data.
Histograms
