1. Descriptive Statistics

2. frequency True class interval 3 49.5-59.5 5 59.5-69.5 18 69.5-79.5 16
89.5
99.5
frequency
frequency
True class interval 3 5 18 16 8 50
total
True class interval

3. Second Lecture Data representation
We will learn in this lecture:
A frequency histogram
A frequency polygon
A frequency curve
A cumulative frequency graph
A steam -and –leaf plot
A bar chart
A line chart
A pie chart
Second Lecture
Data representation

4. Representation of Quantitative Data
A Frequency Histogram
A Frequency Polygon
A Cumulative Frequency Graph
A steam -and –leaf plot

5. Example (1): The following data represent the marks of 50 students in a course:67 90 74 71 73 70 95 51 69 85 84 72 80 50 89 83 91 79 78 75 87 76 82 62 86 57 64 88 81 96 77 66

6. Table (1):frequency table
Class Interval 3
50-59 5
60-69 18
70-79 16
80-89 8
90-99 50
total

7. First:
A Frequency Histogram

8. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

9. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

10. True class interval frequency 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

11. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
frequency
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

12. Secondly:
A Frequency Polygon

13. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

14. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

15. frequency
frequency
True class interval 3 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5

16. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

17. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

18. thirdly
A Frequency Curve

19. frequency True class interval 49.5 59.5 69.5 79.5 89.5 99.5 49.5-59.53 5 18 16 8 50
total
49.5
59.5
69.5
79.5
89.5
99.5
True class interval

20. A-Asceding cumulative frequency Graph (ogive)
Fourthly:
A-Asceding cumulative frequency Graph (ogive)

21. Asceding cumulative frequency distribution
True class intervals 3 5 18 16 8 50
total
frequency
True class intervals
Less than 49.5 3
Less than59.5 8
Less than69.5 26
Less than79.5 42
Less than89.5 50
Less than99.5

22. 49.5 59.5 69.5 79.5 89.5 99.5 frequency Less than 49.5 3 Less than59.5
True class intervals
Less than 49.5 3
Less than59.5 8
Less than69.5 26
Less than79.5 42
Less than89.5 50
Less than99.5
Ascending cumulative frequency
Lower class boundaries
49.5
59.5
69.5
79.5
89.5
99.5

23. 49.5 59.5 69.5 79.5 89.5 99.5 frequency Less than 49.5 3 Less than59.5
True class intervals
Less than 49.5 3
Less than59.5 8
Less than69.5 26
Less than79.5 42
Less than89.5 50
Less than99.5
Ascending cumulative frequency
Lower class boundaries
49.5
59.5
69.5
79.5
89.5
99.5

24. 49.5 59.5 69.5 79.5 89.5 99.5 frequency Less than 49.5 3 Less than59.5
True class intervals
Less than 49.5 3
Less than59.5 8
Less than69.5 26
Less than79.5 42
Less than89.5 50
Less than99.5
Ascending cumulative frequency
Lower class boundaries
49.5
59.5
69.5
79.5
89.5
99.5

25. 49.5 59.5 69.5 79.5 89.5 99.5 frequency Less than 49.5 3 Less than59.5
True class intervals
Less than 49.5 3
Less than59.5 8
Less than69.5 26
Less than79.5 42
Less than89.5 50
Less than99.5
Ascending cumulative frequency
Lower class boundaries
49.5
59.5
69.5
79.5
89.5
99.5

26. 49.5 59.5 69.5 79.5 89.5 99.5 Ascending cumulative frequency
Lower class boundaries
49.5
59.5
69.5
79.5
89.5
99.5

27. B-Desceding cumulative frequency Graph
Fifthly
B-Desceding cumulative frequency Graph

28. Descending cumulative frequency distribution
True class intervals 3 5 18 16 8 50
total
frequency
True class intervals 50
More than 49.5 47
More than 59.5 42
More than 69.5 24
More than 79.5 8
More than 89.5
More than 99.5

29. 49.5 59.5 69.5 79.5 89.5 99.5 frequency True class intervals 50
More than 49.5 47
More than 59.5 42
More than 69.5 24
More than 79.5 8
More than 89.5
More than 99.5
Descending cumulative frequency
49.5
59.5
69.5
79.5
89.5
99.5
Upper class boundaries

30. 49.5 59.5 69.5 79.5 89.5 99.5 frequency True class intervals 50
More than 49.5 47
More than 59.5 42
More than 69.5 24
More than 79.5 8
More than 89.5
More than 99.5
Descending cumulative frequency
49.5
59.5
69.5
79.5
89.5
99.5
Upper class boundaries

31. 49.5 59.5 69.5 79.5 89.5 99.5 frequency True class intervals 50
More than 49.5 47
More than 59.5 42
More than 69.5 24
More than 79.5 8
More than 89.5
More than 99.5
Descending cumulative frequency
49.5
59.5
69.5
79.5
89.5
99.5
Upper class boundaries

32. 49.5 59.5 69.5 79.5 89.5 99.5 Upper class boundaries
Descending cumulative frequency
49.5
59.5
69.5
79.5
89.5
99.5
Upper class boundaries

33. Fifthly: A Steam-And-Leaf Plot

34. A Steam-And-Leaf Plot Example(2):
The following data represent students’ marks in Statistics course: 53 59 58 42 49 46 28 69 67 64 62 66 51 50 78 70 75 68 63 99 93 88 85 84 74

35. 53 59 58 42 49 46 28 69 67 64 62 66 51 50 78 70 75 68 63 99 93 88 85 84 74 2 8 3 4 6 9 2 5 8 9 3 1 6 6 2 4 7 9 3 8 7 9 7 5 8 5 4 8 4 5 8 9 3 9

36. 2 8 3 4 6 9 2 5 8 9 3 1 6 6 2 4 7 9 3 8 7 9 7 5 8 5 4 8 4 5 8 9 3 9

37. Display the data in a steam-and-leaf plot.
Example(3):
Display the data in a steam-and-leaf plot.
38.6
37.9
36.4
36.7
37.5
38.9
32.9
36.8
35.4
35.7
34.2
32.2
32.0
37.2
33.4
32.1
34.6
38.7
38.0
34.5
35.8
36.1
34.4

38. 38.6
37.9
36.4
36.7
37.5
38.9
32.9
36.8
35.4
35.7
34.2
32.2
32.0
37.2
33.4
32.1
34.6
38.7
38.0
34.5
35.8
36.1
34.4 32 9 9 9 2 1 33 4 34 2 4 5 6 35 4 7 7 7 8 36 8 7 4 1 7 37 5 5 9 2 2 38 9 6 7

39. 32 1 2 9 9 9 33 2 4 34 2 4 5 6 35 4 7 7 7 8 36 1 4 7 7 8 37 2 2 5 5 9 38 6 7 9

40. Examples

41. Example(4): Name this plot. What does the vertical axis represent?
What does the horizontal axis represent?
Determine the type of data.
Determine the class width.
Estimate frequencies
Construct the frequency table corresponding to the plot

42. frequency
Mid-points
Class Interval
130 18
140 23
900 28
200 33
790 38
540 43
320 48

43. Example(5): Name this plot. What does the vertical axis represent?
What does the horizontal axis represent?
Determine the type of data.
Determine the class width.
Estimate frequencies
Construct the frequency table corresponding to the plot

44. Lower class boundaries
A.C.f
Lower class boundaries
less than 62 3
less than 64 5
less than 66 10
less than 68 25
less than 70 36
less than 72 44
less than 74 48
less than 76 50
less than 78
frequency
Mid-points
True class interval 3 63
62-64 2 65
64-66 5 67
66-68 15 69
68-70 11 71
70-72 8 73
72-74 4 75
74-76 77
76-78

45. Lower class boundaries
A.C.f
Lower class boundaries
less than 62 3
less than 64 5
less than 66 10
less than 68 25
less than 70 36
less than 72 44
less than 74 48
less than 76 50
less than 78

46. Example (6):
Use the steam-and-leaf plot to list the actual data entries.
What is the maximum data entry?
What is the minimum data entry?
What is the range? 43 41 32 27 50 48 47 44 53 52 51 54 59 58 56 55 78 73 68 85

47. The representation of qualitative data
Line chart
Bar chart
Pie cart

48. Represent the table in a suitable chart
Example(7): The below table shows the number of high schools in KSU from 1395/1396 to 1400/1401 :
1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
year
513 46
407
331
257
212
Number of school
Represent the table in a suitable chart

49. Firstly:
Line Chart

50. 1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
Year
513 46
407
331
257
212
No. School

51. Represent the table in a suitable chart
Example(8): The following table shows the No. of schools in KSA for both genders from 1395/1396 to 1400/1401:
1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
year
375
343
322
273
209
177
No. M
Schools
138
113 85 58 48 35
No. F Schools
Represent the table in a suitable chart

52. 1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
year
375
343
322
273
209
177
No. M schools
138
113 85 58 48 35
No. F schools

53. Secondly:
Bar chart

54. Simple bar chart

55. 1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
year
513 46
407
331
257
212
No. Schools

56. Cluster charts

57. 1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
year
375
343
322
273
209
177
No. M schools
138
113 85 58 48 35
No. F schools

58. Stacked bar chart

59. 1400/1401
1399/1400
1398/99
1397/98
1396/97
1395/96
year
375
343
322
273
209
177
No. M schools
138
113 85 58 48 35
No. F schools

60. Third
Pie charts

61. Central Angle=
frequency x
total of frequencies

62. Example (9): Area (m^2) continent 30.3 Africa 47.4 Asia 4.9 Europe
The following table shows the area of continents to be represented by Pie charts
Area (m^2)
continent
30.3
Africa
47.4
Asia
4.9
Europe
24.3
North America
8.5
Australia
17.9
South America

63. Central Angle
Area (m^2)
continent
30.3
Africa
47.4
Asia
4.9
Europe
24.3
North America
8.5
Australia
17.9
South America
133.3
Total
360

64. Central Angle
Area (m^2)
continent 82
30.3
Africa
128
47.4
Asia 13
4.9
Europe 66
24.3
North America 23
8.5
Australia 48
17.9
South America
360
133.3
Total

65. Realistic studies

70. A frequency histogram
A frequency polygon
A frequency curve
A cumulative frequency graph
A steam -and –leaf plot
A bar chart
A line chart
A pie chart
Summarization