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# Displaying data

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• page 35 of text
• Discussion of what these rating values represent is found on page 33 (the Chapter Problem for Chapter 2).
• Final result of a frequency table on the Qwerty data given in previous slide. Next few slides will develop definitions and steps for developing the frequency table.
• The concept is usually difficult for some students. Emphasize that boundaries are often used in graphical representations of data. See Section 2-3.
• Students will question where the -0.5 and the 14.5 came from. After establishing the boundaries between the existing classes, explain that one should find the boundary below the first class and above the last class, again referencing the use of boundaries in the development of some histograms (Section 2-3).
• Being able to identify the midpoints of each class will be important when determining the mean and standard deviation of a frequency table.
• Class widths ideally should be the same between each class. However, open-ended first or last classes (e.g., 65 years or older) are sometimes necessary to keep from have a large number of classes with a frequency of 0.
• page 38 of text Emphasis on the relative frequency table will assist in development the concept of probability distributions - the use of percentages with classes will relate to the use of probabilities with random variables.
• Some students will need a detailed explanation of how the classes “Less than 3”, “Less than 6”, etc. are identified and the frequency for each of the classes are determined.
• A comparison of all three types of frequency tables developed from the same QWERTY data.
• page 45 of text Data that has at least two digits better exemplifies the value of a stem-leaf plot. Cover up the actual data and ask students to read the data from the stem-leaf plot. Data should be put in increasing order. A stem-leaf plot builds ‘side-ways’ histogram. The most common mistake students make when developing stem-leaf plots is leaving out a ‘stem’ if there is no data in that class. The other mistake is, if there is no data in a class, putting a ‘0’ next to the stem - which, of course, would indicate a data value with a right digit of ‘0’. Students confuse the use of ‘0’ indicating a frequency in a frequency table with a ‘0’ in a stem-leaf plot indicating an actual data value. (See example on page 47 middle of page.)
• A plot of paired (x,y) data with the horizontal x-axis and the vertical y-axis. Chapter 9 will discuss scatter plots again with the topic of correlation. Point out the relationship that exists between the nicotine and tar - as the nicotine value increases, so does the value of tar. page 47 of text
• ### Displaying data

1. 1. A) Tabulation : Frequency distribution Table : - Quantitative - Qualitative B) Drawing: (Graphs / Charts/ Diagrams) Quantitative Data : i) Histogram ii) Frequency Polygon iii) Frequency Curve iv) Line chart /graph v) Cumulative Frequency Diagram / Ogive vi) Scatter or Dot diagram vii) Stem & Leaf plot Qualitative Data : i) Bar diagram (Simple / Multiple / Proportional) ii) Pie or Sector chart iii) Pictogram
2. 2. <ul><li>General principles in designing table : </li></ul><ul><li>The tables should be numbered e.g., Table-1, Table-2 etc. </li></ul><ul><li>There should be a brief and self-explanatory title, mentioning time, place & persons. </li></ul><ul><li>The headings of columns and rows should be clear and concise </li></ul><ul><li>The data must be presented according to size or importance; chronologically, alphabetically or geographically </li></ul><ul><li>Data must be presented meaningfully </li></ul><ul><li>No table should be too large </li></ul><ul><li>Foot notes may be given, if necessary </li></ul><ul><li>Total number of observations (n) i.e the denominator should be written </li></ul><ul><li>The information obtained in the table should be summarized beneath the table </li></ul>
3. 3. TABLE-1 Population by sex in Kolkata urban area in 2001 Source: Health on the March 2004-05, Govt. of West Bengal Characteristics Population (in million) % Male Female 7.07 6.14 53.52 46.48 Total 13.21 100.00
4. 4. Frequency distribution table for qualitative data Characteristics Population (in million) % Male 7.07 53.52 Female 6.14 46.48 Total 13.21 100.00
5. 5. Frequency distribution table for quantitative data Pulse rate/minute No of medical students Percentage 51-60 2 1.33 61-70 22 14.67 71-80 56 37.33 81-90 55 36.67 91-100 14 9.33 101-110 1 0.67 Total 150 100.00
6. 6. <ul><li>Frequency Table </li></ul><ul><li>lists classes (or categories) of values, along with frequencies (or counts) of the number of values that fall into each class </li></ul>2-2 Summarizing Data With Frequency Tables
7. 7. Rating of length measurement Table 2 2 5 1 2 6 3 3 4 2 4 0 5 7 7 5 6 6 8 10 7 2 2 10 5 8 2 5 4 2 6 2 6 1 7 2 7 2 3 8 1 5 2 5 2 14 2 2 6 3 1 7
8. 8. Frequency Table of rating of length Table 2-3 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 rating Frequency
9. 9. Frequency Table Definitions
10. 10. Lower Class Limits <ul><li>are the smallest numbers that can actually belong to different classes </li></ul>
11. 11. Lower Class Limits <ul><li>are the smallest numbers that can actually belong to different classes </li></ul>0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 rating Frequency
12. 12. Lower Class Limits <ul><li>are the smallest numbers that can actually belong to different classes </li></ul>Lower Class Limits 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 rating Frequency
13. 13. Upper Class Limits <ul><li>are the largest numbers that can actually belong to different classes </li></ul>
14. 14. Upper Class Limits <ul><li>are the largest numbers that can actually belong to different classes </li></ul>Upper Class Limits 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 rating Frequency
15. 15. <ul><li>are the numbers used to separate classes, but without the gaps created by class limits </li></ul>Class Boundaries
16. 16. <ul><li>number separating classes </li></ul>Class Boundaries - 0.5 2.5 5.5 8.5 11.5 14.5 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency
17. 17. <ul><li>number separating classes </li></ul>Class Boundaries Class Boundaries <ul><li>0.5 </li></ul><ul><li>2.5 </li></ul><ul><li>5.5 </li></ul><ul><li>8.5 </li></ul><ul><li>11.5 </li></ul><ul><li>14.5 </li></ul>0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency
18. 18. <ul><li>midpoints of the classes </li></ul>Class Midpoints
19. 19. <ul><li>midpoints of the classes </li></ul>Class Midpoints Class Midpoints 0 - 1 2 20 3 - 4 5 14 6 - 7 8 15 9 - 10 11 2 12 - 13 14 1 Rating Frequency
20. 20. <ul><li>is the difference between two consecutive lower class limits or two consecutive class boundaries </li></ul>Class Width
21. 21. <ul><li>is the difference between two consecutive lower class limits or two consecutive class boundaries </li></ul>Class Width Class Width 3 0 - 2 20 3 3 - 5 14 3 6 - 8 15 3 9 - 11 2 3 12 - 14 1 Rating Frequency
22. 22. Relative Frequency Table relative frequency = class frequency sum of all frequencies
23. 23. Relative Frequency Table 20/52 = 38.5% 14/52 = 26.9% etc. Table 2-5 Total frequency = 52 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency 0 - 2 38.5% 3 - 5 26.9% 6 - 8 28.8% 9 - 11 3.8% 12 - 14 1.9% Rating Relative Frequency
24. 24. Cumulative Frequency Table Cumulative Frequencies Table 2-6 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency Less than 3 20 Less than 6 34 Less than 9 49 Less than 12 51 Less than 15 52 Rating Cumulative Frequency
25. 25. Frequency Tables 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency 0 - 2 38.5% 3 - 5 26.9% 6 - 8 28.8% 9 - 11 3.8% 12 - 14 1.9% Rating Relative Frequency Less than 3 20 Less than 6 34 Less than 9 49 Less than 12 51 Less than 15 52 Rating Cumulative Frequency Table 2-6 Table 2-5 Table 2-3
26. 26. Bar Graph <ul><li>The widths of the bar should be equal </li></ul><ul><li>The bars are usually separated by appropriate spaces with an eye to neatness and clear presentation. The spaces between two bars are usually kept equal to the width of the bars. </li></ul><ul><li>The length of the bar is proportional to the frequency. </li></ul><ul><li>A suitable scale must be chosen to present the length of the bars. </li></ul><ul><li>The Y-axis corresponds to the frequency in vertical bar diagram, whereas the X-axis corresponds to the frequency in a horizontal bar diagram </li></ul>
27. 28. Simple Bar Diagram <ul><li>HIV+ve cases in six districts of West Bengal in 2004 </li></ul>Simple ar Diagram each bar represents frequency of a single category with a distinct gap from another bar . .
28. 29. Multiple / Compound Bar diagram show the comparison of two or more sets of related statistical data .
29. 30. Component /Segmented Bar diagram <ul><li>to compare sizes of the different component parts among themselves </li></ul><ul><li>also show the relation between each part and the whole. </li></ul>
30. 31. PIE Diagram <ul><li>Causes of Maternal deaths of West </li></ul><ul><li>Bengal in 2005 </li></ul><ul><li>For for qualitative or discrete data </li></ul><ul><li>Areas of sectors are proportional to frequencies </li></ul><ul><li>Angle (degree) of a sector= </li></ul><ul><li>Class % X3.6, </li></ul><ul><li>Expressing proportional components of the attributes </li></ul><ul><li>compared with that of other segments as well as the whole circle. </li></ul>
31. 32. Histogram <ul><li>A histogram is a bar graph that shows the frequency of each item. Histograms combine data into equal-sized intervals. </li></ul><ul><li>There are no spaces between the bars on the histogram. </li></ul>
32. 34. Line Graph <ul><li>A line graph uses a series of line segments to show changes in data over time. </li></ul><ul><li>Plot a point for each data item, and then connect the dots with straight line segments. </li></ul>
33. 35. Refer to page 336 for the line graph.
34. 36. Frequency Polygon <ul><li>- Frequency </li></ul><ul><li>Distribution graph </li></ul><ul><li>Joining mid-points </li></ul><ul><li>of histogram blocks </li></ul><ul><li>(class intervals) </li></ul><ul><li>When no. of </li></ul><ul><li>observations are </li></ul><ul><li>very large: Frequency </li></ul><ul><li>Polygon loses it’s </li></ul><ul><li>angulations & giving </li></ul><ul><li>a smooth curve: </li></ul><ul><li>Frequency Curve </li></ul>Frequency Distribution Haemoglobin Level
35. 37. Frequency Polygon <ul><li>-Frequency </li></ul><ul><li>polygon presenting </li></ul><ul><li>variations by time </li></ul><ul><li>Trend of an event occurring over a time </li></ul>Year 1901 1911 1921 1951 1961 1971 1941 1931
36. 38. Line Chart or Graph <ul><li>Growth rate in India from 1921-1931 to 1991-2001 </li></ul>the trend of an event occurring over a period of time
37. 39. Ogive (Cumulative frequency polygon <ul><li>to find the median, quartiles, percentiles </li></ul>
38. 40. Stem-and Leaf Plot Raw Data (Test Grades) 67 72 85 75 89 89 88 90 99 100 Stem Leaves 6 7 8 9 10 7 2 5 5 8 9 9 0 9 0
39. 41. <ul><li>Scatter Diagram </li></ul>• • • • • • • • • • • • • • 0 0.0 0.5 1.0 1.5 10 20 • NICOTINE TAR A plot of paired (x,y) data with the horizontal x-axis and the vertical y-axis. will discuss scatter plots again with the topic of correlation. Point out the relationship that exists between the nicotine and tar – as the nicotine value increases, so does the value of tar. • • • • • •