![Respondents and their agreement or
disagreement
• “Mathematics is my favorite course this semester” [five-point interval]
(In the case of 8 items, the scores can range from 8 to 40)
• I strongly agree, 5
• I agree, 4
• I strongly disagree, 3
• I disagree, 2
• I neither agree or disagree, 1
• I don’t know, 0](https://image.slidesharecdn.com/frequencydistributionsgraphinganddatadisplay-180327162820/85/Frequency-distributions-graphing-and-data-display-11-320.jpg)
Frequency distributions, graphing, and data display
- 1. FREQUENCY DISTRIBUTIONS, GRAPHING, AND DATA DISPLAY SUMMARIZING DATA Desmond Ayim-Aboagye, PhD
- 2. SUMMARIES •Tables •Figures •Graphs •What do these teach us?
- 3. 0 1 2 3 4 5 6 Category 1 Category 2 Category 3 Category 4 Chart Title Series 1 Series 2 Series 3 Figures 1. Graphs
- 4. 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 Y-Values Figure 2. Graphs 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 Y-Values
- 5. Type 1 Type 2 40 30 50 40 60 50 Table 1, Type 1 and Type 2
- 6. Sales 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Figure 3, Sales
- 7. Their Importance are that: • Educate and encourage viewers to think about relationships within data. • Sometimes such summaries can spark controversies, leading to creative insights about behavior
- 8. Frequency distribution • Research Methods for Collecting Data • Experiment • Correlational study • Quasi-experiment • 1). Code them 2). Convert them to numbers to enable analysis
- 9. Scales of Measurement (chapt.1) • 1. Nominal • 2. Ordinal • 3. Interval • 4. Ratio • How do we organize and summarize them?
- 10. Frequency distribution • A frequency distribution is a table presenting the number of participant responses (e.g., scores, values) within the numerical categories of some scale of measurement.
- 11. Respondents and their agreement or disagreement • “Mathematics is my favorite course this semester” [five-point interval] (In the case of 8 items, the scores can range from 8 to 40) • I strongly agree, 5 • I agree, 4 • I strongly disagree, 3 • I disagree, 2 • I neither agree or disagree, 1 • I don’t know, 0
- 12. x f fx 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 1 0 0 0 1 1 1 2 1 1 2 1 0 1 0 1 0 0 5 1 1 1 0 1 0 0 1 0 1 0 4 40 0 0 0 36 35 34 66 32 31 60 29 0 27 0 25 0 0 110 21 20 19 0 17 0 0 14 0 12 0 40 (40 x 1 = 40) ( 39 x 0 = 0 ) ( 38 x 0 = 0) ( 37 x 0 = 0) (36 x 1 = 36) ( 35 x 1 = 35) ( 34 x 1 = 34) ( 33 x 2 = 66) ( 32 x 1 = 32) ( 31 x 1 = 31) ( 30 x 2 = 60) ( 29 x 1 = 29) ( 28 x 0 = 0) (27 x 1 = 27) ( 26 x 0 = 0) ( 25 x 1 = 25) ( 24 x 0 = 0) ( 23 x 0 = 0) (22 x 5 = 110) (21 x 1 = 21) ( 20 x 1 = 20) ( 19 x 1 = 19) (18 x 0 = 18) (17 x 1 = 17) ( 16 x 0 = 0) ( 15 x 0 = 0) (14 x 1 = 14) ( 13 x 0 = 0) ( 12 x 1 = 12) (11 x 0 = 0) ( 10 x 4 = 40) Table 3.2 Frequency Distribution for Life Orientation Test (LOT) Scores
- 13. Frequency data • Frequency distributions simplify data for quick study. When they are constructed well, no valuable information is lost. • Suppose N = 30 • Scores = x • Σ𝑓 = N • Σ𝑓.x = Σ𝑓𝑥 • See Table 3 in your book
- 14. Proportion and percentages • A proportion is a number reflecting a given frequency (f) relationship to the N of the available sample or group. It is a fractional value of the total group associated with each individual score. • Proportion = p= f/N • that is frequency divided by total number of the group or sample N (1÷30 =0.033) • It percentage 0.033 x 100 = 3%
- 15. Relative frequency distribution for LOT scores • P = f/N adding all gives 1.00 • P (100) = 100% • A relative frequency distribution indicates the percent or proportion of participants who received each of the raw scores of x.
- 16. Class Intervals of x f 37-40 33-36 29-32 25-28 21-24 17-20 13-16 9-12 5-8 1 5 5 2 6 3 1 6 1 Σ𝑓 = 30 Table 3.5 Revised Group Frequency Distribution for LOT Scores Note: The Intervals in this table are based on the frequency distribution shown in Table 3.2, which in turn is based on the raw scores from Table 3.1.
- 17. Class Intervals of x f 36.5-40.5 32.5-36.5 28.5-32.5 24.5-28.5 20.5-24.5 16.5-20.5 12.5-16.5 8.5-12.5 4.5-8.5 1 5 5 2 6 3 1 6 1 Σf = 30 Table 3.6 Grouped frequency distribution of LOT scores with true limits and class intervals Note: The intervals in this table are based on the frequency distribution shown in Table 3.2, which in turn is based on the raw scores from Table 3.1.
- 18. Constructing Intervals and Scores • Caution • Are all the class intervals the same width? They should be the same. • Do any class intervals overlap with one another? They should not. • Do all data fit into the table? There should be no leftover scores.
- 19. Graphing Frequency Distributions • A graph is a diagram illustrating connections or relationships among two or more variables. Graphs are often made up of connecting lines or dots.
- 20. Figure 3.2 The Two Axes (x and y) used for graphing data Higher values for y Y Axis or Ordinate Lower values for y y Lower values for x X Axis or Abscissa Higher values for x x
- 21. 0 2 4 6 8 10 12 14 Female Male Heterosexual Homosexual Bar Graphs Series 1 Series 2 Series 3 Figure 1. Bar graphs of surveys returned by respondents gender Y X
- 22. 0 2 4 6 8 10 12 14 Year 1 Year 2 Year 3 Year 4 Figure 1. Graph comparing the prices of 3 commodities in 4 years Pinaples Tobacco Sugar Cane Prices in Thousand Dollars X axis Y axis
- 23. SHAPE OF DISTRIBUTIONS • Frequency distributions can come in any number of varieties shapes. But only one is ideal for performing statistical analyses. • Normal distribution. • A normal distribution is a hypothetical, bell-shaped curve wherein the majority of observations appear at or near the midpoint of the distribution. • Skew distribution • This refers to a non-symmetrical distribution whose observations cluster at one end.
- 24. Skinny and quasi-normal (leptokurtic) Normal (mesokurtic) Fatter curve (platykurtic)
- 25. A positively skewed distribution A bimodal distribution Negatively skewed distribution
- 26. Percentiles and Percentile Ranks • A Percentile rank is a number indicating what percentage of scores fall at or below a given score on a measure. • A score of 75% of an exam is a bout ¾. So when an individual gets 30 score of the exams which is 75% (i.e., ¾) we say that she had 75th percentile.
- 27. Cumulative Frequency • A Cumulative frequency refers to the number of values within a given interval added to the total number of values that fall below that interval. • Cumulative frequencies are organized into what are called cumulative frequency distributions.
- 28. Class Intervals of X f Cf % C% 36.5-40.5 32.5-36.5 28.5- 32.5 24.5- 28.5 20.5- 24.5 16.5- 20.5 12.5- 16.5 8.5- 12.5 4.5- 8.5 1 5 5 2 6 3 1 6 1 30 29 24 19 17 11 8 7 1 3.33 16.67 16.67 6.67 20.00 10.00 3.33 20.00 3.33 100 96.67 80.00 63.33 56.67 36.67 26.67 23.33 3.33 Σ𝑓 = 30 Table 3.9 Cumulative Frequency Distribution of LOT Scores with Limits and Class Intervals
- 29. Cumulative Percentage • Cumulative Percentage = cumulative frequency/total no of scores x100 • Example cf of 17 will be 17/30 x 100 = 56.67%
- 30. Quartile • Q 1, Q 2, Q3, and Q3. • When a data distribution is divided into four equal parts, each part is labeled a quartile.