| 5.2.1 |
Types of data |
|
| 1. |
Quantitative (numerical) data |
|
a) Discrete data |
|
e.g. number of students in a class;
number of variables in a program. |
|
b) Continuous data |
|
e.g. height of a person; the time
to taken to complete an examination. |
| 2. |
Qualitative (categorical) data |
|
e.g. sex of a student, presence
or absence in a class. |
|
|
|
| 5.2.2 |
Raw data |
|
Data recorded in the sequence in
which they are collected and before they are processed or ranked are called
raw data. |
|
Example 5.2-1
Suppose that the numbers of hours
that students spend in working with computer per week are recorded in the
following table. |
|
Table 5.1 Hours spend in
working with computer per week |
|
|
21
|
19
|
24
|
25
|
22
|
19
|
|
22
|
19
|
19
|
25
|
22
|
25
|
|
23
|
19
|
23
|
26
|
22
|
28
|
|
21
|
25
|
23
|
18
|
27
|
23
|
|
18
|
19
|
22
|
21
|
19
|
17
|
|
|
|
| 5.2.3 |
Frequency distributions |
|
A population is a collectA much
more informative presentation of the data in table5.1 is an arrangement
called a simple frequency distribution. Table 5.2 is a simple frequency
distribution. It is an arrangement that shows the frequency of each
hour. |
|
Table 5.2 Frequency distribution
of numbers of hours working with computer |
|
|
Hour (x)
|
Tally marks
|
Frequency ( f )
|
|
17
|
/
|
1
|
|
18
|
//
|
2
|
|
19
|
/////
//
|
7
|
|
20
|
|
0
|
|
21
|
///
|
3
|
|
22
|
/////
|
5
|
|
23
|
////
|
4
|
|
24
|
/
|
1
|
|
25
|
////
|
4
|
|
26
|
/
|
1
|
|
27
|
/
|
1
|
|
28
|
/
|
1
|
|
|
|
| 5.2.4 |
Relative frequency and percentage
distributions |
|
A relative frequency distribution
lists the relative frequencies for all categories. The relative frequency
of a category is obtained by using the following formula. |
|
|
|
A percentage distribution lists
the percentages for all categories. The percentage for a category
is obtained by multiplying the relative frequency of that category by 100.
i.e. |
|
Percentage = Relative frequency
x
100
|
|
Example 5.2-2
Table 5.3 shows the frequency, relative
frequency and percentage distribution of a particular piece of information. |
|
Table 5.3 Frequency,
relative frequency and percentage distribution. |
|
|
Department
|
Frequency
|
Relative Frequency
|
Percentage
|
|
Business
|
6
|
6 / 36
= 0.17
|
0.17 x
100% = 17%
|
|
Computing
|
8
|
8 / 36
= 0.22
|
0.22 x
100% = 22%
|
|
Engineering
|
6
|
6 / 36
= 0.17
|
0.17 x
100% = 17%
|
|
Mathematics
|
4
|
4 / 36
= 0.11
|
0.11 x
100%
= 11%
|
|
Others
|
12
|
12 / 36
= 0.33
|
0.33 x
100% = 33%
|
|
Total
|
36
|
1.00
|
100%
|
|
|
|
| 5.2.5 |
Grouped frequency distributions |
|
When the size of raw data becomes
large, it would be appropriate to group the data into classes. Data
presented in the form of a frequency distribution are called grouped data. |
|
Example 5.2-3
Table 5.4 shows the number of computer
keyboards assembled of a company for a sample of 25 days. |
|
Table 5.4 Number of
keyboards assembled. |
|
|
Classes
|
Frequency
|
|
41 - 50
|
5
|
|
51 - 60
|
8
|
|
61 - 70
|
8
|
|
71 - 80
|
4
|
|
|
Lower and upper limit |
|
The smallest value in a class is
called the lower limit of the class. e.g. 41, 51, 61, 71 and 81.
The largest value in a class is
called the upper limit of the class. e.g. 50, 60, 70 and 80. |
|
Class midpoint |
|
The midpoint of a class is obtained
by using the following formula. |
|
|
|
e.g. 45.5, 55.5, 65.5 and 75.5. |
|
Class boundary |
|
The class boundary is given by the
midpoint of the upper limit of one class and the lower limit of the next
class. e.g. 50.5, 60.5 and 70.5. |
|
Class width |
|
The class width is obtained by using
the following formula. |
|
|
|
e.g. 60.5 - 50.5 = 10 |
|
|
| 5.2.6 |
Constructing grouped frequency
distribution tables |
|
Number of classes |
|
Usually the number of classes for
a frequency distribution table varies from 5 to 20, depending mainly on
the number of observations in the data set. It is preferable to have
more classes as the size of a data set increase. e.g. there are four
classes in Table 5.4. |
|
Class width |
|
Although it is not uncommon to have
classes of different sizes, most of the time it is preferable to have the
same width for all classes. To determine the class width when all
classes are of the same size, the approximate width of a class is obtained
by using the following formula |
|
|
|
Usually this approximate class width
is rounded to a convenient number.
e.g. the class width of the data
in Table 5.4 is (50 - 41 + 1) = 10. |
|
Starting point |
|
Any convenient number which is equal
to or less than the smallest value in the data set can be used as the lower
limit of the first class. |
|
Example 5.2-4
Construct a grouped frequency distribution
table for the following hourly output rate data. |
|
Table 5.5 Hourly output
rate. |
|
|
81
|
76
|
78
|
84
|
76
|
78
|
|
79
|
80
|
79
|
76
|
82
|
84
|
|
73
|
78
|
73
|
74
|
72
|
86
|
|
77
|
80
|
83
|
82
|
83
|
79
|
|
75
|
80
|
83
|
81
|
77
|
79
|
|
|
Approximate width of a class
Therefore, class width = 3
Starting value = 72 |
|
Table 5.6 Frequency
and percentage distributions table. |
|
|
Output Rate
|
Tally
|
Frequency
|
Boundary
|
Relative Frequency
|
Percentage
|
|
72 - 74
|
////
|
4
|
71.5 to
< 74.5
|
0.133
|
13.3
|
|
75 - 77
|
/////
/
|
6
|
74.5 to
< 77.5
|
0.200
|
20.0
|
|
78 - 80
|
/////
/////
|
10
|
77.5 to
< 80.5
|
0.333
|
33.3
|
|
81 - 83
|
//////
//
|
7
|
80.5 to
< 83.5
|
0.233
|
23.3
|
|
84 - 86
|
///
|
3
|
83.5 to
< 86.5
|
0.100
|
10.0
|
|
Total
|
|
30
|
|
0.999
|
99.9%
|
|
|
|
