1 / 40

SUMMARIZING DATA

SUMMARIZING DATA. THROUGH TABLES AND GRAPHS. FOR QUALITATIVE DATA (2.1). FREQUENCY DISTRIBUTION TABLES FREQUENCY DISTRIBUTION GRAPHS. DEFINITIONS. Frequency Distribution: Lists each category (label) of data and the number of occurrences. Sum of all = population or sample size

zenaida-buck
Download Presentation

SUMMARIZING DATA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SUMMARIZING DATA THROUGH TABLES AND GRAPHS

  2. FOR QUALITATIVE DATA (2.1) • FREQUENCY DISTRIBUTION TABLES • FREQUENCY DISTRIBUTION GRAPHS

  3. DEFINITIONS • Frequency Distribution: Lists each category (label) of data and the number of occurrences. • Sum of all = population or sample size • Relative Frequency: The proportion of occurrences for each category calculated as: Sum of all = 1.

  4. DEFINITIONS • Bar Graph: Vertical or Horizontal. X-axis contains the categories or labels. For Frequency Distributions the y-axis is the number of occurrances. For Relative Frequency Distributions the y-axis is the proportion (values between 0 and 1). Bars do not need to be touching.

  5. BAR GRAPHS

  6. FREQUENCY DISTRIBUTION TABLESOF QUALITATIVE DATA

  7. READING DATA FROM GRAPHS

  8. COMPARISONS USING GRAPHS

  9. PARETO CHART

  10. READING BAR GRAPHS

  11. EXAMPLE USING COLOR OF EYES

  12. PIE CHARTS

  13. FOR QUANTIATIVE DATA (2.2) • CAN TREAT DISCRETE DATA LIKE QUALITATIVE (IF ONLY SEVERAL VALUES) OR AS WE WILL BE TREATING CONTINUOUS DATA (IF MANY VALUES) • SEPARATE CONTINUOUS DATA INTO CLASSES (INTERVALS) AND THEN DO DISTRIBUTION TABLES OR GRAPHS

  14. DEFINITIONS FOR QUANTIATIVE DATA DISRTIBUTIONS Frequency Distribution Table: Similar to that for qualitative data, but each class is for a value or an interval (range) of values. Histograms: Vertical bar graphs, where the x-axis is the number line and each bar is for a class. All bars must touch side to side. Uses Lower Class limit on x-axis.

  15. OTHER FREQUENCY DISTRIBUTIONS • Cumulative Frequency Distributions: Each class listed as before (lowest to largest), but the frequencies are the total for that frequency and all the lower classes. • Relative Cumulative Frequency Distribution: Each Cumulative Frequency divided by total of all frequencies. The last class will have a cumulative value of 1.0

  16. EXAMPLES OF DISCRETE DATA • Use number of siblings • Do as Frequency Table • Do as Relative Frequency • Do as Cumulative Frequency • Do as Relative Cumulative Frequency

  17. FREQUENCY DISTRIBUTION OF CONTINUOUS DATA - DEFINITIONS • Class: An interval of numbers along the number line. • Lower Class Limit (LCL): The beginning number of the class. • Upper Class Limit (UCL): The last number of the class.

  18. FREQUENCY DISTRIBUTION OF CONTINUOUS DATA - DEFINITIONS • Class Width: the difference between lower class limits (or upper class limits), found by taking using data set’s maximum and minimum and calculating rounding up to a convenient value • Midpoint of Each Class: The point in the middle of the class, found by averaging the class lower class limit and the next class lower class limit.

  19. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 1. Organize data in ascending order:

  20. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 2. Determine the number of classes (5 – 20): For this we will use 6. 3. Find the maximum and minimum: For this max = 4.91 and min = 1.03

  21. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 4. Calculate the Class Width: Round UP to a convenient value. We will use 0.70.

  22. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 5. Determine First Lower Class Limit: For this we will use 1.00 (something convenient and lower than the Minimum). 6. Determine the next 5 Lower Class Limits by adding class width to the first and each subsequent to get the next: 1.00+.70=1.70; 1.70+.70=2.40 … 3.10, 3.80, 4.50.

  23. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 7. Determine the first Upper Class Limit by Subtracting 1 from the last place of the second Lower Class Limit: 1.70-.01=1.69. 8. Find the other 5 Upper Class Limits by adding the class width to each previous Upper Class Limits: 1.69+.7=2.39, 2.39+.7=3.09, …, 3.79, 4.49, 5.19

  24. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 9. Now construct the Table ……:

  25. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE And count the frequencies in each class …:

  26. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE And complete the Table:

  27. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 10. Draw the histogram:

  28. CREATE FREQUENCY DISTRIBUTION FOR CONTNUOUS DATA: EXAMPLE 2

  29. OTHER DISTRIBUTION PLOTS • Stem Leaf Plot: Used for recording and showing dispersion of data. Stem can be the integer portion of a number and the leaves the decimal portion. Or the stem could be the tens digit and the leaves the ones digit. • 5-3,5,6,7,7,8,9 • 6-2,3,3,4,6,6,7,8 • 7-1,1,3,6,9

  30. OTHER DISTRIBUTION PLOTS • Dot Plot: Also used to show dispersion of data. Draw a number line and label the horizontal scale with the numbers from the data from lowest to highest. Then place a dot above the numbers each time the number occurs. * * * * * * * * * * |___|___|___|___|___|___|___|___|___|___| 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3

  31. OTHER DISTRIBUTION PLOTS (2.3) • Polygon Plot: Line graph using the midpoints for the x-axis and frequencies for the y-axis. Both ends of the line must come back to the 0 on the y-axis.

  32. OTHER DISTRIBUTION PLOTS

  33. OTHER DISTRIBUTION PLOTS • Given a Polygon Plot, construct a Frequency Distribution Table. • 1. Find the Class Width: Difference in Midpoints • 2. Find first two LCL’s: Midpoint +/- ½*Class Width • 3. Find First Upper Class Limit: 2nd LCL – 1 • Find remainder of LCL’s & UCL’s • Find each class’s frequency

  34. OTHER DISTRIBUTION PLOTS • Ogive (pronounced oh jive) Plot: Line Graph used for displaying Cumulative Frequency Distributions. The x-axis is the Upper Class Limit and the y-axis is the Cumulative Frequency. The first point is a class width less than the first Upper Class Limit so that the line starts with a frequency of 0.

  35. OTHER DISTRIBUTION PLOTS • Ogive Plot:

  36. OTHER DISTRIBUTION PLOTS • Time Series Plots: Can be vertical or horizontal bar graphs, or line graphs. X-axis is time intervals or ages (years, months, days) and y-axis is frequency.

  37. TYPES OF DISTRIBUTION

  38. TYPES OF DISTRIBUTION

  39. MISREPRESENTATIONS OF DATA USING GRAPHS (2.4) • Vertical Scale Manipulation: Not starting the y-axis at 0. Also using a break in the scale. Can make differences look bigger than they really are. • Exaggeration of Bars or Symbols: Used in pictographs. • Horizontal Scale Manipulation: Not all classes or time interval are the same width.

  40. MISREPRESENTATIONS OF DATA USING GRAPHS • “Get your facts first, then you can distort then as you please” Mark Twain • “There are lies, damn lies, and STATISTICS” Mark Twain • “Definition of Statistics: The science of producing unreliable facts from reliable figures.” Evan Esar

More Related