Statistics
Organizing the Data
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Sasmita JatiBob Septian
NidiaNovi Dwi P
FairusM. Zuhri
Frequency distributions of nominal data and
Comparing Distribution
Frequency distributions of nominal data
The researchers-aided by ‘recipes’ called formulas
and statistical techniques - attempts to transform raw
data into a meaningful and organized set of
measures that can be used to test hypotheses.
Constructing a frequency distribution in
the form of a table is the first researcher’s
step to organize the jumble of raw
numbers that they collect from their
subject.
Table 2.1 Respnses of young boys to removal of toy
Response of child F Cry 25 Express anger 15 Withdraw 5 Play with another toy 5 N = 50
Comparing DistributionMaking comparisons between frequency distributions is a
procedure often used to clarify results and add information.
The particular comparison a researcher makes is to determined
by the question he or she seeks to answer.
Table 2.2 Response to removal of toy by gender of child
Response of child Gender of child male female
Cry 25 28 Express anger 15 3 Withdraw 5 4 Play with another toy 5 15
Total 50 50
Proportions and PercentagesThe proportion compares the number of cases in a given category with the total size of the distribution.
P P : Proportionf : the number of case
N : Total case in distribution
Percentage
To calculate percentage, we simply multiply any given proportion by 100.
%
Percentile
Ranks
Find the percentile rank for a score of 92 in the following score distribution !
Class Interval f % cf c%
90-99 6 12.24 49 100
80-89 8 16.33 43 87.76
70-79 12 24.49 35 71.43
60-69 10 20.41 23 46.94
50-59 7 14.29 13 26.53
40-49 6 12.24 6 12.24
N 49 100
1st
StepClass Interval f % cf c%
90-99 6 12.24 49 100
80-89 8 16.33 43 87.76
70-79 12 24.49 35 71.43
60-69 10 20.41 23 46.94
50-59 7 14.29 13 26.53
40-49 6 12.24 6 12.24
N 49 100
Finding Critical Interval
Critical interval is the interval in which the data you want to find its percentile ranks is exist.
9290-91-92-93-94-95-96-97-
98-99
2nd
StepClass Interval f % cf c%
90-99 6 12.24 49 100
80-89 8 16.33 43 87.76
70-79 12 24.49 35 71.43
60-69 10 20.41 23 46.94
50-59 7 14.29 13 26.53
40-49 6 12.24 6 12.24
N 49 100
Finding The lower limit of Critical Interval
• “…class limits are located at the point halfway between adjacent class intervals..”
89.590 – 0.5 =
3rd Step
Class Interval f % cf c%
90-99 6 12.24 49 100
80-89 8 16.33 43 87.76
70-79 12 24.49 35 71.43
60-69 10 20.41 23 46.94
50-59 7 14.29 13 26.53
40-49 6 12.24 6 12.24
N 49 100
Finding The Size of Critical Interval
1090-91-92-93-94-95-96-97-99
4th Step
Class Interval f % cf c%
90-99 6 12.24 49 100
80-89 8 16.33 43 87.76
70-79 12 24.49 35 71.43
60-69 10 20.41 23 46.94
50-59 7 14.29 13 26.53
40-49 6 12.24 6 12.24
N 49 100
Finding The percentage within critical interval
%
5th Step
Class Interval f % cf c%
90-99 6 12.24 49 100
80-89 8 16.33 43 87.76
70-79 12 24.49 35 71.43
60-69 10 20.41 23 46.94
50-59 7 14.29 13 26.53
40-49 6 12.24 6 12.24
N 49 100
The cumulative percentage below critical interval
%
The cumulative
percentage below
critical interval
89.5
12.26 %
The lower limit of Critical Interval
The Size of Critical Interval 10
The percentage within critical interval
87.76 %
PR = percentile rank
c%b = cumulative percentage below the lower limit of the critical intervalX = raw score under considerationL = lower limit of the critical intervalI = class interval size% = percentage within critical interval
PR = c%b + %
PR = percentile rank
c%b = cumulative percentage below the lower limit of the critical intervalX = raw score under considerationL = lower limit of the critical intervalI = class interval size% = percentage within critical interval
87.76 % + (
92 – 89.5
) 10
=90.82
12.26
90.82WHAT DOES IT
MEAN??
WHAT iS IT
for??
Percentile Rank
91 - 10081 - 9071 - 8061 - 7051 - 6041 - 5031 - 4021 - 3011 - 201 – 10
Decile
Quartile
76 – 10051 – 75 26 – 50 1 - 25
10th9th8th
7th6th5th4th3rd2nd1st
4th3rd 2nd 1st
Percentile Rank
90.82
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