Frequency Distributions & Graphs

1. Frequency Distributions & Graphs

2. Descriptive Statistics • The goal of descriptive statistics is to summarize a collection of data in a clear and understandable way. • What is the pattern of scores over the range of possible values? • Where, on the scale of possible scores, is a point that best represents the set of scores? • Do the scores cluster about their central point or do they spread out around it?

3. What is the pattern of scores? • Create a Frequency Distribution • Frequency distributions organize raw data or observations that have been collected. • Ungrouped Data • Listing all possible scores that occur in a distribution and then indicating how often each score occurs. • Grouped Data • Combining all possible scores into classes and then indicating how often each score occurs within each class. • Easier to see patterns in the data, but lose information about individual scores.

4. Las Vegas Hotel Rates

5. Las Vegas Hotel Rates

6. Las Vegas Hotel Rates An Example: GroupedFrequency Distribution • Find the lowest and highest score (order scores from lowest to highest). • 891 is highest score. • 52 is lowest score. • Find the range by subtracting the lowest score from the highest score. • 891-52 = 839 • Divide range by 10. • 839/10 = 83.9 • Round off to the nearest convenient width. • 100 • Determine the scores at which the lowest interval should begin (an interval of the class width). • 0

7. An Example: Grouped Frequency Distribution • Record the limits of all class intervals, placing the interval containing the highest score value at the top. • Count up the number of scores in each interval. Hotel Rates Frequency Las Vegas Hotel Rates 800-899 1 700-799 4 600-699 2 500-599 0 400-499 6 300-399 8 200-299 8 100-199 4 0-99 2

8. Frequency Table Guidelines • Intervals should not overlap, so no score can belong to more than one interval. • Make all intervals the same width. • Make the intervals continuous throughout the distribution (even if an interval is empty). • Place the interval with the highest score at the top. • For most work, use 10 class intervals. • Choose a convenient interval width. • When possible, make the lower score limit a multiple of the interval width. • Sum to N

9. An Example: Grouped Frequency Distribution • Proportion (Relative Frequency) • Divide frequency of each class by total frequency. Hotel Rates Frequency Proportion 1/35=.03 800-899 1 .03 700-799 4 .11 600-699 2 .06 500-599 0 0 400-499 6 .17 300-399 8 .23 200-299 8 .23 100-199 4 .11 0-99 2 .06 N = 35 Σ= 1.0

10. An Example: Grouped Frequency Distribution • Cumulative Frequency: sum of each frequency and all below it • Cumulative Proportion (Cumulative Relative Frequency): • Divide Cumulative Frequency by Total Frequency • Percentile Rank • Cumulative Proportion * 100 35/35= 34/35=

11. What is the pattern of scores? • Graphs often make it easier to see certain characteristics and trends in a set of data. • Graphs for quantitative data. • Stem and Leaf Display • Histogram • Frequency Polygon • Graphs for qualitative data. • Bar Chart • Pie Chart number/count class/category

12. Raw data 14 24 36 73 52 35 15 24 35 33 34 66 11 14 54 56 24 35 75 43 17 67 26 31 40 29 10 43 27 49 16 9 35 77 28 34 19 64 10 56 Stem Leaf 9 0 1 2 3 4 5 6 7 001445679 4446789 134455556 0339 2466 467 357

16. Histogram • Consists of a number of bars placed side by side. • The width of each bar indicates the interval size. • The height of each bar indicates the frequency of the interval. • There are no gaps between adjacent bars. • Continuous nature of quantitative data.

17. Histogram

18. Shapes of Histograms

19. Frequency Polygons • Uses a single point rather than a bar

20. Bar Graph

21. Pie Graph

22. Misleading Graphs