Data presentation

Prepared byAssis. Prof.

Namir G. Al-Tawil

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.

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.

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.

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.

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

Figure 1. Success rate by college

0

10

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60

70

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90

Erbil Sulaimany DuhokCollege

Succ

ess

rate

%

Age (years)

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2

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17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5

freq

uenc

y

The Frequency Polygon

Distribution of Sample by Age

Line Graph

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10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69

Age (years)

fre

que

ncy

Figure 1. Distribution of sample by sex

Males, 150, 33%

Females, 300, 67%