2. Learning
objectives
§ At the end of this session you will be able to:
• Present qualitative data using tabular methods
• Present qualitative data using graphical methods
• Present quantitative data using tabular methods
• Present quantitative data using graphical
methods
2
3. Descriptive
summary statistics
§ Descriptive statistics: Techniques used to
organize and summarize a set of data in more
comprehensible and meaningful way
– Organization of data
– Summarization of data
– Presentation of data
§ Numbers that have not been summarized and
organized are called raw data
3
4. Raw data
Definition
§ Data that have been collected or recorded but
have not been arranged or processed yet are
called raw data
4
6. Example2:
§ These are types of blood group for a sample of
50 OPD patients
O AB A AB AB B O B B O
O O B O A O O A B B
A A AB O O O A O O B
A O O O A B O O A A
O A A B AB B O A O A
9. Frequency
Distribution
§ Frequency distribution: is a table that summarizes
a raw data into non-overlapping classes or categories
along with their corresponding class frequency
§ Class frequency: The number of observations that
fall into the class
§ The objective is to provide insights about the data
that cannot be quickly obtained by looking only at the
original data
9
10. Frequency
Distribution
§ The actual summarization and organization of
data starts from frequency distribution
§ The distribution condenses the raw data into a
more useful form and allows for a quick visual
interpretation of the data
10
11. Frequency Distribution
for categorical variables
§ Count the number of observations (frequency) in
each category and present as relative
frequencies
§ Often presented in the form of Table, Bar and
Pie charts
11
12. Frequency Distribution for
categorical variables
§ Relative frequency: value for any category
obtained by dividing the number of observations in
that category by the total number of observations
- Class relative frequency = Class frequency/
Total number of observations
§ This can be reported as a percentage by
multiplying the resulting fraction by 100
12
13. Frequency Distribution
for categorical variables
§ A relative frequency distribution: Shows the proportion
of counts that fall into each class or category
§ For nominal and ordinal data, frequency distributions
are often used as a summary
§ The % of times that each value occurs, or the relative
frequency, is often listed
§ Tables make it easier to see how the data are
distributed
13
14. Example 1: Nominal data
Table 1: Type of hospitals owned by MOH in Ethiopia
in 2006/07
Source: Health and health related indicator
14
15. Example 2: Ordinal data
Table 2: Level of satisfaction, with nursing care by
475 psychiatric in-patients, 1991
15
16. Frequency Distribution
for numerical variables
§ A frequency distribution can also show the number
of observations at different values or within
certain ranges
§ There are two types of frequency distribution:
– Single value (ungrouped frequency)
– Interval type (classes) – grouped frequency
16
17. Ungrouped Frequency
Distribution
§ Ungrouped frequency distribution: Consists
of a single data with their respective frequency
§ Can be used when the range of values in the
data set is not large
§ Classes are one unit in width
17
18. Example:
§ Leisure time in hours per week for 40 college
students:
23 24 18 14 20 36 24 26 23 21 16 15 19 20
22 14 13 10 19 27 29 22 38 28 34 32 23 19
21 31 16 28 19 18 12 27 15 21 25 16
Construct a frequency distribution table?
18
20. Grouped Frequency
Distribution
§ Can be used when the range of values in the
data set is large
§ The data must be grouped into classes that are
more than one unit in width
20
21. Grouped Frequency
Distribution
§ Steps in Constructing Frequency Distribution
Tables
Step 1: Determine the range of the data
- R = Highest Value – Lowest Value
21
22. Step 2: Determine the number of classes (k) and
the corresponding width, we may use:
Where;
K = number of class intervals n = no. of observations
W = width of the class interval L = the largest value
S = the smallest value
22
23. Step 3: For each class, count the number of
observations (class frequency)
Step 4: Determine the relative frequency for each
class
Frequency of each class interval
Relative frequency =
Total number of observations
23
27. § Cumulative frequencies: When frequencies of
two or more classes are added
§ Cumulative relative frequency: The proportion of
the total number of observations that have a value
less than or equal to the upper limit of the interval
§ Mid-point: The value of the interval which lies
midway between the lower and the upper limits of
a class
27
28. § True limits: Are those limits that make an
interval of a continuous variable continuous in
both directions
§ Used for smoothening of the class intervals
§ Subtract 0.5 from the lower and add it to the
upper limit
28
30. Guidelines for
constructing tables
§ Tables should be self-explanatory
§ Include clear title telling what, when and where
§ Clearly label the rows and columns
§ State clearly the unit of measurement used
§ Explain codes and abbreviations in the foot-note
§ Show totals
§ If data is not original, indicate the source in foot-
note
30
31. Graphical
presentation of data
§ Help users to obtain at a glance an intuitive feeling
of the data
§ Should be self-explanatory
§ Must have a descriptive title, labeled axes and
indication of the units of measurement
31
32. Graphical
presentation
Importance of Graphical presentation:
§ Diagrams have greater attraction than mere figures
§ They give quick overall impression of the data
§ They have great memorizing value than mere
figures
§ They facilitate comparison
§ Used to understand patterns and trends
32
33. Graphical
presentation
§ Well designed graphs can be powerful means of
communicating a great deal of information
§ When graphs are poorly designed, they not only
ineffectively convey message, but they are often
misleading
33
34. Types of graphs
§ Categorical data
– Bar chart
– Pie-chart
§ Quantitative data
– Histogram
– Frequency Polygon
– Ogive
– Stem-and-leaf plot
– Box plot
– Scatter Diagram
34
35. Bar chart
Definition:
§ A graph made of bars whose heights represent
the frequencies of respective categories is called
a bar graph.
35
36. Bar chart
§ Used to display frequency contained in the
frequency distribution of categorical variable
§ It is used with categorical data
§ Each bar represent one category and its height is
the frequency or relative frequency
o y – axis: Frequency or the relative
frequency or percentage
o x – axis: Category
36
37. Bar chart
Rules
o Bars should be separated
o The gap between each bar is uniform
o All bars should be of the same width
o All the bars should rest on the same line called the
base
o It is very important that Y axis begin with 0
o Label both axes clearly
37
38. Simple bar chart
38
40.6
53.9
5.5
0
10
20
30
40
50
60
First trimester Second trimester Third trimester
Percentage
Series1
Figure 1 : First ANC booking time among pregnant women in X
Town, Ethiopia, 2017
§The simple bar chart is appropriate if only one
variable is to be shown
39. Clustered bar chart
39
Urban Rural
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
Percent
Residence
First day
Second and subsquent days
25.7
74.3
10.0
90
Figure 2 : Timing of health care seeking reported by place of
residence, X District, Ethiopia, 2011.
40. Pie-chart
A pie chart: is a circle that is divided into
sections according to the percentage of
frequencies in each category of the distribution
§ Used for a single categorical variable relative
frequency
§ Each slice of pie correspond at relative
frequency of categories of variable
40
41. Pie-chart
Steps to construct a pie-chart
§ Construct a frequency table
§ Change the frequency into percentage (P)
§ Change the percentages into degrees, where:
degree = Percentage X 360o
§ Draw a circle and divide it accordingly
41
43. Histogram
§ Histograms are frequency distributions with
continuous class intervals that have been
turned into graphs
§ To construct a histogram, we draw the interval
boundaries on a horizontal line and the
frequencies on a vertical line
43
44. Histogram
§ In a histogram, the bars are drawn adjacent to
each other
§ The bars are drawn to touch each other, to show
the underlying continuity of the data
§ In a histogram, the area of each bar is proportional
to the frequency of observations in the interval
44
45. Example
Total Home Runs f
124 – 145
146 – 167
168 – 189
190 – 211
212 - 233
6
13
4
4
3
§Using the following frequency distribution of the
home runs hit by Major League Baseball teams
during the 2002 season, construct the histogram
45
46. Total Home
Runs
Class Boundaries Frequency
Cumulative
frequency
124 – 145
146 – 167
168 – 189
190 – 211
212 - 233
123.5 - 145.5
145.5 - 167.5
167.5 - 189.5
189.5 - 211.5
211.5 - 233.5
6
13
4
4
3
6
19
23
27
30
Total 30
§ Class boundaries and their Frequency and
cumulative frequency distributions
46
48. Frequency
polygon
§ Frequency polygon: Is a graph formed by joining
the midpoints of the tops of successive bars in a
histogram with straight lines
§ The total area under the frequency polygon is
equal to the area under the histogram
48
50. Ogive
§ Ogive: Is a curve drawn for the cumulative
frequency distribution by joining with straight lines
the dots marked above the upper boundaries of
classes at heights equal to the cumulative
frequencies of respective classes
50
51. Ogive
§ It is obtained as follows:
On a vertical axis we mark cumulative frequency
On a horizontal axis we mark the upper
boundaries of all classes. However, the lower
boundary of the first class will be the starting
point
Then, a smooth curve is drawn joining all these
points
51
52. Total Home
Runs
Class Boundaries Frequency
Cumulative
frequency
124 – 145
146 – 167
168 – 189
190 – 211
212 - 233
123.5 - 145.5
145.5 - 167.5
167.5 - 189.5
189.5 - 211.5
211.5 - 233.5
6
13
4
4
3
6
19
23
27
30
Total 30
§ Class boundaries and their Frequency and
cumulative frequency distributions
52
53. Ogive
123.5 145.5 167.5 189.5 211.5 233.5
30
25
20
15
10
5
Figure 6: Total home runs hit by all players of each of the 30
Major League Baseball teams during the 2002 season
Cumulative
frequency
53
54. Stem-and leaf plot
® Another common tool for visually displaying
continuous data is the “stem and leaf” plot
® Allows for easier identification of individual values
in the sample
® Very similar to a histogram
® Are most effective with relatively small data sets
® Helps to understand the nature of data
– Presence or absence of symmetry
54
55. Stem-and leaf plot
§ Can be constructed as follows:
(1) Separate each data point into a stem component
and a leaf component
The stem component consists of the number
formed by all but the rightmost digit of the
number, and the leaf component consists of the
rightmost digit. Thus the stem of the number
483 is 48, and the leaf is 3
(2) Write the smallest stem in the data set in the
upper left-hand corner of the plot
55
56. Data of birth weights from 100 consecutive
deliveries
56
58. Stem-and-leaf plot can be constructed as
follows:
(3) Write the second stem, which equals the fist stem
+ 1, below the fist stem
(4) Continue with step until you reach the largest stem
in the data set
(5) Draw a vertical bar to the right of the column of
stems
(6) For each number in the data set, find the
appropriate stem and write the leaf to the right of
the vertical bar
58
59. § One way to give a nice profile of a data set is the
box plot
§ Gives good insight into distribution shape in terms
of skewness and outlying values
§ Very nice tool for easily comparing distribution of
continuous data in multiple groups—can be plotted
side by side
Box plot
59
60. Box plot: BP for 113 Males
Boxplot of Systolic Blood Pressures
Sample of 113 Men
60
61. Box plot: BP for 113 Males
Sample Median
Blood Pressure
Box plot of Systolic Blood Pressures
Sample of 113 Men
61
62. Box plot: BP for 113 Males
75th Percentile
25th Percentile
Boxplot of Systolic Blood Pressures
Sample of 113 Men
62
63. Box plot: BP for 113 Males
Largest Observation
Smallest Observation
Boxplot of Systolic Blood Pressures
Sample of 113 Men
63
64. Tabular and Graphical Procedures
Qualitative Data Quantitative Data
Tabular
Methods
Tabular
Methods
Graphical
Methods
Graphical
Methods
Data
64
