Graphical Representation of Data.pdf
- 1. Qualitative data Example 1: Consider the data about Sex of 10 students • Make a frequency distribution, relative frequency and % frequency of the above data and interpret your results? Make an appropriate graph? Example 2: Suppose we have also collected data of Sections of these 10 students as • Construct the Cross tabulation of the above data and interpret your results? Also make an appropriate graph? M F M M F M F M M M M F M M F M F M M M A A A B B B A B A B Sex Sex Section
- 2. Solution Sex f Relative freq % freq Male 7 0.7 70 Female 3 0.3 30 Total 10 1.0 100 7 3 0 1 2 3 4 5 6 7 8 Male Female Frequency Sex Bar Chart Sex Sec A Sec B Total Male 3 4 7 Female 2 1 3 Total 5 5 10 0 1 2 3 4 5 Male Female Frequency Sex Multiple Bar chart Sec A Sec B Example 1 Example 2
- 3. Simple Bar Chart • A bar chart is a type of chart which shows the values of different categories of data as rectangular bars with different lengths. Example: Draw a Simple Bar Chart to represent the Population of 5 cities of the province Punjab. Cities Population (000) Lahore 10,355 Rawalpindi 4,765 Faisalabad 3,675 Sargodha 1,550 Multan 3,100 10,355 4,765 3,675 1,550 3,100 0 2,000 4,000 6,000 8,000 10,000 12,000 Lahore Rawalpindi Faisalabad Sargodha Multan Population in ‘000’ Cities Bar diagram showing Population of 5 cities of Punjab
- 4. Multiple Bar Chart 5385 2478 1911 806 4,970 2,287 1,764 744 0 1000 2000 3000 4000 5000 6000 Lahore Rawalpindi Faisalabad Sargodha POPULATION CITIES Multiple Bar Chart showing Population of Males and Females Males Females Cities Population (000) Male Female Lahore 10,355 5385 4,970 Rawalpindi 4,765 2478 2,287 Faisalabad 3,675 1911 1,764 Sargodha 1,550 806 744
- 5. Component Bar Chart 5385 2478 1911 806 4,970 2,287 1,764 744 0 2000 4000 6000 8000 10000 12000 Lahore Rawalpindi Faisalabad Sargodha Population Cities Component Bar Chart showing population of both Males and Females and Total Males Females Cities Pop (000) Male Female Lahore 10,355 5385 4,970 Rawalpindi 4,765 2478 2,287 Faisalabad 3,675 1911 1,764 Sargodha 1,550 806 744
- 6. Discrete data – Frequency Distribution Example: • Following data represents the number of infected plants from a sample of twenty experimental plots. Your task is to present it in tabular form. 1 2 4 3 0 1 2 3 1 1 0 2 1 0 2 3 0 0 1 3
- 7. Discrete Frequency Distribution No. of infected items X 0 1 2 3 4 Total Relative frequency 5/20 = 0.25 0.30 0.20 0.20 0.05 1.00 Frequency f 5 6 4 4 1 20 Tally |||| |||| | |||| |||| |
- 8. Graphical Representation of Discrete Data 5 6 4 4 1 0 1 2 3 4 5 6 7 0 1 2 3 4 Frequency No. of infected items Bar Chart representing the infected items
- 9. Pie Chart • A pie chart is a type of graph in which a circle is divided into sectors that each represent a proportion of the whole. Example: The blood group of 70 students were tested and the following results were obtained. Blood Groups No. of Students (f) A 8 B 30 O 20 AB 12 11% 43% 29% 17% Blood Groups of Students A B O AB
- 10. Pie Chart Blood Groups No. of Students (f) A 8 B 30 O 20 AB 12 Total 70 Relative frequency 8/70 = 0.11 0.43 0.29 0.17 1.00 Percent frequency 0.11*100 = 11 43 29 17 100 Angle rf x 360 39.6 154.8 104.4 61.2 360 Divide the total angle of the Circle 360 into four segments as calculated
- 11. Simple Bar Chart • Consider the Same example of the blood group of 70 students Blood Groups No. of Students (f) A 8 B 30 O 20 AB 12 8 30 20 12 0 5 10 15 20 25 30 35 A B O AB Blood Groups
- 12. Following data represents the plant height (cm) of a sample of 30 plants. 87 91 89 88 89 91 87 92 90 98 95 97 96 100 101 96 98 99 98 100 102 99 101 105 103 107 105 106 107 112 Classes Frequency (f) c.f. r.f. % freq 86–90 6 6 0.200 20.0 91–95 4 10 0.133 13.3 96–100 10 20 0.333 33.3 101–105 6 26 0.200 20.0 106–110 3 29 0.100 10.0 111–115 1 30 0.033 3.3 Total 30 1.000 100.0 6 4 10 6 3 1 0 2 4 6 8 10 12 85.5–90.5 90.5–95.5 95.5–100.5 100.5–105.5 105.5–110.5 110.5–115.5 Frequency Class Boundries Histogram Frequency distribution & Histogram
- 13. Frequency Distribution Classes 86–90 91–95 96–100 101–105 106–110 111–115 Total Class Boundaries 85.5–90.5 90.5–95.5 95.5–100.5 100.5–105.5 105.5–110.5 110.5–115.5 Tally Freq (f) 6 4 10 6 3 1 30 c.f. 6 10 20 26 29 30 r.f. 0.200 0.133 0.333 0.200 0.100 0.033 1.000 % freq 20.0 13.3 33.3 20.0 10.0 3.3 100.0 Cumulative % freq 20.00 33.3 66.6 86.6 96.6 100.0
- 14. Class Boundaries • Class Boundaries • Subtract any Upper Class Limit from its Subsequent Lower Class limit and divide the difference with 2, you will get the Continuity correction factor • Subtract this factor from all Lower Class Limits and add it to all Upper Class limits. For example, 91-90 = ½ =0.05 or 96-95 = ½ =0.05
- 15. Histogram 6 4 10 6 3 1 0 2 4 6 8 10 12 85.5–90.5 90.5–95.5 95.5–100.5 100.5–105.5 105.5–110.5 110.5–115.5 Frequency Class Boundries Histogram of Height of 30 Students
- 16. Frequency Polygon • Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data. • Mid Points vs Frequency 0 2 4 6 8 10 12 88 93 98 103 108 113 Frequency Mid Points Frequency Polygon
- 17. Cumulative Frequency Polygon / Ogive • A cumulative frequency polygon is a plot of the cumulative frequency against the upper class boundary with the points joined by a line segment. • Upper Class Boundaries vs Cumulative Frequency 0 5 10 15 20 25 30 35 90.5 95.5 100.5 105.5 110.5 115.5 Cumulative Frequency Upper Class Boundaries Cumulative Frequency Polygon / Ogive
- 18. Stem & Leaf Display • A relatively small data set can be represented by stem and leaf display. • In addition to information on the number of observations falling in the various classes, it displays details of what those observations actually are. • Each number in the data set is divided into two parts, a Stem and a Leaf. A stem is the leading digit(s) of each number and is used in sorting, while a leaf is the rest of the number or the trailing digit(s) and shown in display.
- 19. Example Represent the following data by Stem and Leaf display by (i) taking 10 unit as the width of the class (ii) taking 5 unit as the width of the class 32 45 38 41 49 36 52 56 51 62 63 59 68 Steam 3 4 5 6 Leaf 2 8 6 5 1 9 2 6 1 9 2 3 8 Steam 3* 3. 4* 4. 5* 5. 6* 6. Leaf 2 8 6 1 5 9 2 1 6 9 2 3 8 *indicate 0—4 .indicate 5—9 * and . are called placeholder
- 20. Example Use the data below to make a stem- and-leaf plot by taking 10 as a unit. 85 115 126 92 104 85 116 100 121 123 79 90 110 129 108 Stem 7 8 9 10 11 12 13 Leaf 0 5 8 9 4 5 5 8 0 2 2 3 7 9 0 4 7 8 0 4 5 6 6 1 3 6 9 1 1 2 7 0 5 8 9 These values are 70, 75, 78 and 79 107 78 131 114 92 131 88 97 99 116 93 84 75 70 132