3. Types of Data
Quantitative data are measurements that are recorded
on a naturally occurring numerical scale.
Exp. Height in cm. ,weight in kg. ,blood pressure
(mm/Hg)
Qualitative data are measurements that cannot be
measured on a natural numerical scale; they can only be
classified into one of a group of categories.
Exp . Sex, tall or short, blood group
3
5. Class Frequency, f
1 – 4 4
5 – 8 5
9 – 12 3
13 – 16 4
17 – 20 2
Frequency Distributions
A frequency distribution is a table that shows classes or
intervals of data with a count of the number in each
class. The frequency f means the number of times a
certain value of variable is repeated.
Frequencies
5
6. Class Frequency, f
1 – 4 4
5 – 8 5
9 – 12 3
13 – 16 4
17 – 20 2
Class width
The class width is the distance between lower (or
upper) limits of consecutive classes.
The class width is 3.
4 – 1 = 3
8 – 5 = 3
12 – 9 = 3
13-16=3
6
7. Guidelines
1. Condense the data by classifying them in to groups or
classes called as class intervals..
2. It is best to select class intervals of equal size.
3. Find the class width
4. Find the class limits. You can use the minimum entry
as the lower limit of the first class. To find the
remaining lower limits, add the class width to the
lower limit of the preceding class. Then find the upper
class limits.
5. Make a tally mark for each data entry in the row of the
appropriate class.
7
8. CONT………..
6. Count the tally marks to find the total frequency f for
each class.
7. Class limits are specially started either inclusive or
exclusive manner.
8. Inclusive manner- 45-49;50-54;55-59….
9. Excusive manner-45-50;50-55;55-60….
10.Interval may be represented by midpoints of class
interval.
8
9. Constructing a Frequency Distribution
18 20 21 27 29 20
19 30 32 19 34 19
24 29 18 37 38 22
30 39 32 44 33 46
54 49 18 51 21 21
Example:
The following data represents the ages of 30 students in a
statistics class. Construct a frequency distribution that
has five classes.
Ages of Students
9
10. Constructing a Frequency Distribution
Example continued:
250 – 57
342 – 49
434 – 41
826 – 33
1318 – 25
Tally Frequency, fClass
30f
Number
of
students
Ages
Check that
the sum
equals the
number in
the sample.
Ages of Students
10
11. Midpoint
The midpoint of a class is the sum of the lower and
upper limits of the class divided by two. The midpoint is
sometimes called the class mark.
Midpoint = (Lower class limit) + (Upper class limit)
2
Frequency, fClass Midpoint
41 – 4
Midpoint =
1
2
4 5
2
2.5
2.5
11
12. Relative Frequency
Class Frequency, f
Relative
Frequency
1 – 4 4
The relative frequency of a class is the portion or
percentage of the data that falls in that class. To find the
relative frequency of a class, divide the frequency f by
the sample size n.
Relative frequency =Class frequency
Sample size
Relative frequency 8
4
1
0.222
0.222
f
n
18f
f
n
12
13. Cumulative Frequency
The cumulative frequency of a class is the sum of the
frequency for that class and all the previous classes.
30
28
25
21
13
Total number
of students
+
+
+
+50 – 57 2
3
4
8
13
42 – 49
34 – 41
26 – 33
18 – 25
Frequency, fClass
30f
Cumulative
Frequency
Ages of Students
13
14. Graphical &Diagrammatic Presentation
• It provides a visual method of examining quantitative
and qualitative data.
• It brings out clear and relative importance of different
figures and helpful in finding out relation between
two or more sets of data.
a. Presentation of qualitative data:
A. Bar diagrams
B. Line diagrams
C. Pie diagrams
14
15. CONT………
D. Pictograms.
E. Map diagrams.
b. Presentation of quantitative data
A. Histogram
B. Frequency polygon
C. Cumulative frequency curve or ogive
D. Scattered diagram
15
18. (C)The Pie Chart
CC
18
Marital Status Frequency %
Single 20 28
Married 30 41
Divorced 10 14
Widowed 12 17
Total 72 100
Distribution of a group of subjects by marital status
21. 21
Presentation of quantitative data
1.The Histogram
Examples:
Age in Years Number of patients
0 - 5 4
5 - 10 10
10 - 15 18
15 - 20 8
20 - 25 6
Total 46
23. 23
2.The Frequency Polygon
• Examples:
Age in Years Sex Mid-point of interval
Males Females
20-30 (20+30)/2=25
30-40 (30+40)/2=35
40-50 (40+50)/2=45
50-60 (50+60)/2=55
60-70 (60+70)/2=65
Total
24. The Frequency Polygon
• Example:
Figure (2): Distribution of a group of subjects by age and sex
24
25. 25
3.Cumulative Frequency Graph
A cumulative frequency graph or ogive, is a line graph that
displays the cumulative frequency of each class at its upper class
boundary.
17.5
Age (in years)
Ages of Students
24
18
12
6
30
0
Cumulativefrequency
(portionofstudents)
25.5 33.5 41.5 49.5 57.5
The graph ends at
the upper
boundary of the
last class.
26. 26
Class Boundaries
Example:
Find the class boundaries for the “Ages of Students” frequency distribution.
49.5 57.5
41.5 49.5
33.5 41.5
25.5 33.5
17.5 25.5The distance from the
upper limit of the first
class to the lower limit
of the second class is 1.
Half this distance
is 0.5.
Class Boundaries
50 – 57 2
3
4
8
13
42 – 49
34 – 41
26 – 33
18 – 25
Frequency, fClass
30f
Ages of Students
27. 27
4.The Scatter Diagram
• When two quantitative variables such as blood pressure and weight
have been measured on the same set of individuals, a simple and
effective way of describing them is the scatter diagram.
• Each individual’s X (first variable value) and y (2nd variable value)
measurements are plotted as a point on the diagram.
• The X value plotted on the horizontal scale.
• The Y value on the vertical scale.
• For example for the data below, the first individual’s weight is 67 kg,
his blood pressure is 114 mmHg.
• The marked point in the figure corresponds to this individual's weight
and blood pressure.
Weight (kg) 67 69 85 83 74 81 97 92 114
SBP (mmHg) 114 90 88 96 113 92 103 123 125
28. 28
The Scatter diagram
Weight (kg) 67 69 85 83 74 81 97 92 114
SBP (mmHg) 114 90 88 96 113 92 103 123 125
Scatter diagram of weight and systolic blood pressure for a group of individuals
