This document discusses methods for organizing and summarizing data, including ordered arrays, frequency distributions, and frequency polygons. An ordered array lists values from smallest to largest. A frequency distribution groups observations into class intervals to summarize the data, with 6-15 intervals typically used. Sturge's rule provides a formula for calculating the number of intervals. The width of intervals should be equal if possible. A example frequency distribution table with age data in intervals is provided. Figures also demonstrate a success rate by college graph and frequency polygon displaying age data.

1. Data presentation
Prepared by
Assis. Prof.
Namir G. Al-Tawil

2. The ordered array
 It is the first step in the process of data
organization.
 An ordered array is a listing of values of a
collection in order of magnitude from the
smallest value to the largest value.
 It enables one to determine quickly the
value of the smallest measurement, and
the value of the largest measurement, and
enable one to determine roughly the
proportion of people lying below or above
certain value.

6. The frequency distribution
 One of the ways of data summarization.
 To group a set of observations, we
select a set of class intervals. There
must be no overlapping between these
intervals.
 Too few intervals are undesirable
because of the resulting loss of
information. If too many intervals are
used, the objective of summarization
can not be met. The appropriate No. of
class intervals is 6-15.

7. The frequency distribution, cont.
 Sturge’s rule (formula):
K = 1 + 3.322 (log10 n)
K = No. of class intervals. n = sample size.
 Note that this rule is not final, you can
increase or decrease the No. of class
intervals for convenience and clear
presentation.

8. The frequency distribution, cont.
 The width (W) of class interval, in general,
is equal, but sometimes this is not possible.
 W = R/K
 R = Range (difference between smallest
and largest observation).
 For convenience, a width of 5 units or 10
units is used.

9. Example of a frequency distribution
table of 169 subjects of different
ages
Class
interval
Frequency Cumulative
frequency
Relative
frequency
Cumulative R.
Frequency
10-19 4 4 0.0237 0.0237
20-29 66 70 0.3905 0.4142
30-39 47 117 0.2781 0.6923
40-49 36 153 0.2130 0.9053
50-59 12 165 0.0710 0.9763
60-69 4 169 0.0237 1.0000
Total 169 1.0000

14. Figure 1. Success rate by college
0
10
20
30
40
50
60
70
80
90
Erbil Sulaimany Duhok
College
Successrate%

20. Age (years)
0
1
2
3
4
5
6
17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5
frequency
The Frequency Polygon

21. Distribution of Sample by Age
Line Graph
0
10
20
30
40
50
60
70
10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69
Age (years)
frequency

22. Figure 1. Distribution of sample by sex
Males, 150, 33%
Females, 300, 67%