This document discusses methods for presenting tabular and graphical data summaries. It covers constructing frequency distributions for grouped and ungrouped data, and different types of graphs that can be used to summarize quantitative and qualitative data, including histograms, frequency polygons, ogives, stem and leaf plots, pie charts, and bar charts. Examples are provided for constructing frequency distributions and different graph types.

2. Tabular and Graphical Presentation of Data
Lecture | 2

3. • Construct a frequency distribution: grouped and ungrouped data
• Various types of frequency distribution and its application
• Construct graphical summaries of qualitative data
• Construct graphical summaries of quantitative data
• Construct graphical summaries of two variables
Learning Objectives

4. • Ungrouped Data
 have not been summarized in any way
 are also called raw data
• Grouped Data
 logical groupings of data exists
i.e. age ranges (20-29, 30-39, etc.)
 have been organized into a frequency distribution
Ungrouped Versus
Grouped Data

5. 42
30
53
50
52
30
55
49
61
74
26
58
40
40
28
36
30
33
31
37
32
37
30
32
23
32
58
43
30
29
34
50
47
31
35
26
64
46
40
43
57
30
49
40
25
50
52
32
60
54
Ages of 50 patients arrived
on a particular date at Abha
Private Hospital
Example of
Ungrouped Data

6. • Frequency Distribution – summary of data presented in the form of
class intervals and frequencies
– Vary in shape and design
– Constructed according to the individual researcher's preferences
Frequency
Distribution

7. Steps in Frequency Distribution
• Step 1 - Determine range of frequency distribution
• Range is the difference between the high and the lowest numbers
• Step 2 – determine the number of classes
• Don’t use too many, or two few classes
Frequency
Distribution

8. • Step 3 – Determine the width of the class interval
• Approx class width can be calculated by dividing the
range by the number of classes
• Values fit into only one class
Frequency
Distribution

9. Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
Frequency Distribution of
patient’s age arrived at
hospital

10. Relative
Class Interval Frequency Frequency
20-under 30 6 .12
30-under 40 18 .36
40-under 50 11 .22
50-under 60 11 .22
60-under 70 3 .06
70-under 80 1 .02
Total 50 1.00
6
50

18
50

The relative frequency is the proportion of the total frequency
that is any given class interval in a frequency distribution.
Relative Frequency

11. The cumulative frequency is a running total of frequencies
through the classes of a frequency distribution.
Cumulative
Class Interval Frequency Frequency
20-under 30 6 6
30-under 40 18 24
40-under 50 11 35
50-under 60 11 46
60-under 70 3 49
70-under 80 1 50
Total 50
18 + 6
11 + 24
Cumulative Frequency

12. Cumulative
Relative Cumulative Relative
Class Interval Frequency Frequency Frequency Frequency
20-under 30 6 .12 6 .12
30-under 40 18 .36 24 .48
40-under 50 11 .22 35 .70
50-under 60 11 .22 46 .92
60-under 70 3 .06 49 .98
70-under 80 1 .02 50 1.00
Total 50 1.00
The cumulative relative frequency is a running total of the relative
frequencies through the classes of a frequency distribution.
Cumulative Relative Frequencies

13. • Histogram -- vertical bar chart of frequencies.
• Frequency Polygon -- line graph of frequencies
• Ogive -- line graph of cumulative frequencies
• Stem and Leaf Plot – Like a histogram, but shows individual data
values. Useful for small data sets.
Common Statistical Graphs –
Quantitative Data

14. • A histogram is a graphical summary of a frequency
distribution
• The number and location of bins (bars) should be
determined based on the sample size and the range of
the data
Histogram

15. 42
30
53
50
52
30
55
49
61
74
26
58
40
40
28
36
30
33
31
37
32
37
30
32
23
32
58
43
30
29
34
50
47
31
35
26
64
46
40
43
57
30
49
40
25
50
52
32
60
54
Smallest
Largest
51
=
23
-
74
=
Smallest
-
Largest
=
Range
Data Range

16. 10
=
Width
Class
8.5
=
6
51
=
Class
Num
Range
=
Width
Class
Approx
• The number of classes should be between 5 and 15.
– Fewer than 5 classes cause excessive summarization.
– More than 15 classes leave too much detail.
• Class Width
– Divide the range by the number of classes for an approximate class width
– Round up to a convenient number
Number of Classes and
Class Width

17. Class Midpoint =
beginning class endpoint + ending class endpoint
2
=
30 + 40
2
= 35
 
Class Midpoint = class beginning point +
1
2
class width
= 30 +
1
2
10
= 35
The midpoint of each class interval is called the
class midpoint or the class mark.
Class Midpoint

18. Relative
Cumulative
Class Interval Frequency Midpoint Frequency Frequency
20-under 30 6 25 .12 6
30-under 40 18 35 .36 24
40-under 50 11 45 .22 35
50-under 60 11 55 .22 46
60-under 70 3 65 .06 49
70-under 80 1 75 .02 50
Total 50 1.00
Class Midpoint

19. Class IntervalFrequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
Histogram

20. Class IntervalFrequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
0
10
20
0 10 20 30 40 50 60 70 80
Years
Frequency
Histogram
Construction

21. Class IntervalFrequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
0
5
10
15
20
Frequency
Years
Frequency Polygon

22. Cumulative
Class Interval Frequency
20-under 30 6
30-under 40 24
40-under 50 35
50-under 60 46
60-under 70 49
70-under 80 50
0
20
40
60
0 10 20 30 40 50 60 70 80
Years
Frequency
Ogive

23. Cumulative
Relative
Class Interval Frequency
20-under 30 .12
30-under 40 .48
40-under 50 .70
50-under 60 .92
60-under 70 .98
70-under 80 1.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
0 10 20 30 40 50 60 70 80
Years
Cumulative
Relative
Frequency
Relative Frequency Ogive

24. 86
76
23
77
81
79
68
77
92
59
68
75
83
49
91
47
72
82
74
70
56
60
88
75
97
39
78
94
55
67
83
89
67
91
81
Raw Data Stem
2
3
4
5
6
7
8
9
Leaf
3
9
7 9
5 6 9
0 7 7 8 8
0 2 4 5 5 6 7 7 8 9
1 1 2 3 3 6 8 9
1 1 2 4 7
Stem and Leaf plot:
Example

25. 86
76
23
77
81
79
68
77
92
59
68
75
83
49
91
47
72
82
74
70
56
60
88
75
97
39
78
94
55
67
83
89
67
91
81
Raw Data Stem
2
3
4
5
6
7
8
9
Leaf
3
9
7 9
5 6 9
0 7 7 8 8
0 2 4 5 5 6 7 7 8 9
1 1 2 3 3 6 8 9
1 1 2 4 7
Stem
Leaf
Stem
Leaf
Construction of Stem and Leaf Plot

26. • So, which one should I use?
• A Stem and Leaf plot is useful for small data sets. It shows the values of
the data points.
• A histogram foregoes seeing the individual values of the data for the
bigger picture of the distribution of the data
• The purpose of these graphs is to summarize a set of data. As long as
that need is met, either one is okay to use.
Histogram vs. Stem and Leaf ?

27. • Pie Chart -- proportional representation for categories of a whole
• Bar Chart – frequency or relative frequency of one more
categorical variables
Common Statistical
Graphs – Qualitative Data

28. COMPLAINT NUMBER PROPORTION DEGREES
Aseer Hospital 28,000 .40 144.0
Abha Private
Hospital
14,700 .21 75.6
Saudi German
Hospital
10,500 .15 50.4
Military Hospital 9,800 .14 50.6
Maternity Hospital 7,000 .10 36.0
Total 70,000 1.00 360.0
Average patient arrived per year at five
major hospital of Aseer region

29. Average patient arrived per year at five
major hospital of Aseer region
Aseer Hospital
40%
Abha Private
Hospital
21%
Saudi Germa
Hospital
15%
Militry
Hospital
14%
Maternity Hospital
10%
Number of Patient per year

30. Number of cases at
different hospital
(Hypothetical values)
Number of
cases
Hospital
A
B
C
D
E
Totals
357,411
354,936
160,997
34,099
12,747
920,190
Number of cases at different
hospital

31. 39%
17%
4%
1%
39%
A B C D E
Number of cases at different
hospital

32. 2d Quarter
Truck
Production Proportion Degrees
Company
A
B
C
D
E
Totals
357,411
354,936
160,997
34,099
12,747
920,190
.388
.386
.175
.037
.014
1.000
140
139
63
13
5
360
357,411
920,190
=
=
360
.388
Pie Chart Calculations for
Company A