1. Chapter 2 CREATING AND USING FREQUENCY DISTRIBUTIONS

2. Going Forward Your goals in this chapter are to learn: What frequency is and how a frequency distribution is created When to graph frequency distributions using a bar graph, histogram, or polygon What normal, skewed, and bimodal distributions are What relative frequency and percentile are and how we use the area under the normal curve to compute them

3. New Symbols and Terminology Raw scores are the scores we initially measure in a study The number of times a score occurs in a set of data is the score’s frequency A frequency distribution organizes the scores based on each score’s frequency

4. New Symbols and Terminology The frequency of a score is symbolized by f N is the total number of scores in the data

5. Understanding Frequency Distributions

6. Frequency Distribution A frequency distribution table shows the number of times each score occurs in a set of data N is the total of all the individual frequencies in the f column of a frequency distribution table

7. Raw Scores Use the following raw scores to construct a frequency distribution table. 14 13151115 131012131413 14151714 15

8. Frequency Distribution Table

9. Graphing Frequency Distributions A frequency distribution graph always shows the scores on the X axis and their frequency on the Y axis The type of measurement scale (nominal, ordinal, interval, or ratio) determines whether we use – A bar graph – A histogram – A polygon

10. Frequency Bar Graph for Nominal and Ordinal Data

11. Histogram for a Small Number of Different Interval or Ratio Scores

12. Frequency Polygon for Many Different Interval or Ratio Scores

13. Types of Frequency Distributions

14. The Normal Distribution A bell-shaped curve Called a normal curve or a normal distribution Symmetrical The far left and right portions containing the relatively low-frequency, extreme high or low scores are called the tails of the distribution

15. An Ideal Normal Distribution

16. Skewed Distributions A skewed distribution is not symmetrical as it has only one pronounced tail A distribution may be either negatively skewed or positively skewed The direction in which the distinctive tail slopes indicates whether the skew is positive or negative

17. Negatively Skewed Distribution A negatively skewed distribution contains extreme low scores having low frequency, but does not contain low- frequency, extreme high scores.

18. Positively Skewed Distribution A positively skewed distribution contains extreme high scores having low frequency, but does not contain low- frequency, extreme low scores.

19. Bimodal Distribution A bimodal distribution is a symmetrical distribution containing two distinct humps.

20. Frequency Distribution Shape The shape of the frequency distribution is an important characteristic of the data The shape also determines which statistical procedures we should use

21. Relative Frequency and the Normal Curve

22. Relative Frequency Relative frequency is the proportion of the time a score occurs in a sample The formula for computing a score’s relative frequency is Relative frequency =

23. Finding Relative Frequency Using the Normal Curve The proportion of the total area under the normal curve occupied by a group of scores corresponds to the relative frequency of those scores.

24. Understanding Percentile and Cumulative Frequency

25. Percentile A percentile is the percent of all scores in the data located below a score One way to determine a score’s percentile is to find the area under the normal curve to the left of the score

26. Cumulative Frequency The cumulative frequency is the number of scores in the data that are at or below a particular score.

27. Percentiles Normal distribution showing the area under the curve to the left of selected scores.

28. Example Using the following data set, find the relative frequency and cumulative frequency of the score 12. 14 13151115 131012131413 14151714 15

29. Example The frequency table for this set of data.

30. Example—Relative Frequency The frequency for the score of 12 is 1 and N = 18 Therefore, the relative frequency of 12 is Relative Frequency

31. Example—Cumulative Frequency There is one score at 12 and two scores below 12 (one score of 11 and one score of 10) Therefore, the cumulative frequency of 12 is 3