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Organizi
the Data
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SasmitaJati
BobSeptian
Nidia
NoviDwiP
Fairus
M.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.
Comparing Distribution
Making 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.
Proportions and Percentages
The proportion compares the number of cases in a given
category withthetotal size of the distribution.
P=
𝑓
𝑁
P: Proportion
f: the number of case
N: Total case in distribution
Percentage
To calculate percentage,we simplymultiplyany given
proportion by 100.
% = 100
𝑓
𝑁
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
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 Critical
Interval
Critical interval is
the interval in
which the data
you want to find
its percentile
ranks is exist.
92
90-91-92-93-94-95-96-97-
98-99
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 lower limit of
Critical
Interval
• “…class limits
are located at
the point
halfway
between
adjacent class
intervals..”
89.590 –
0.5 =
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
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
% =
100
𝑓
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
% =
100
𝑐𝑓
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
interval
X= raw score under consideration
L= lower limit of the criticalinterval
I= class interval size
%= percentage within critical interval
PR = c%b +
𝑋−𝐿
𝑖
%
PR = percentile rank
c%b = cumulative percentage below the lower limit of the critical
interval
X= raw score under consideration
L= lower limit of the criticalinterval
I= class interval size
%= percentage within critical interval
87.76
%
+
(
92 –
89.5
)10
12.26
Percentile
Rank
91 - 100
81 - 90
71 - 80
61 - 70
51 - 60
41 - 50
31 - 40
21 - 30
11 - 20
1 – 10
Decil
e
Quartile
76 – 100
51 – 75
26 – 50
1 - 25
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
1st
4th
3rd
2nd
1st
Percentile
Rank

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Organizing The Data

  • 2. Frequency distributions of nominal data and Comparing Distribution
  • 3. 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.
  • 4. 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.
  • 5.
  • 6. Comparing Distribution Making 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.
  • 7.
  • 8. Proportions and Percentages The proportion compares the number of cases in a given category withthetotal size of the distribution. P= 𝑓 𝑁 P: Proportion f: the number of case N: Total case in distribution
  • 9. Percentage To calculate percentage,we simplymultiplyany given proportion by 100. % = 100 𝑓 𝑁
  • 10.
  • 11. 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
  • 12. 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 Critical Interval Critical interval is the interval in which the data you want to find its percentile ranks is exist. 92 90-91-92-93-94-95-96-97- 98-99
  • 13. 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 lower limit of Critical Interval • “…class limits are located at the point halfway between adjacent class intervals..” 89.590 – 0.5 =
  • 14. 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
  • 15. 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 % = 100 𝑓
  • 16. 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 % = 100 𝑐𝑓
  • 17. 89. 5 12.26 % The lower limit of Critical Interval The Size of Critical Interval 10 The percentage within critical interval 87.76 %
  • 18. PR = percentile rank c%b = cumulative percentage below the lower limit of the critical interval X= raw score under consideration L= lower limit of the criticalinterval I= class interval size %= percentage within critical interval PR = c%b + 𝑋−𝐿 𝑖 %
  • 19. PR = percentile rank c%b = cumulative percentage below the lower limit of the critical interval X= raw score under consideration L= lower limit of the criticalinterval I= class interval size %= percentage within critical interval 87.76 % + ( 92 – 89.5 )10 12.26
  • 20.
  • 21. Percentile Rank 91 - 100 81 - 90 71 - 80 61 - 70 51 - 60 41 - 50 31 - 40 21 - 30 11 - 20 1 – 10 Decil e Quartile 76 – 100 51 – 75 26 – 50 1 - 25 10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st 4th 3rd 2nd 1st Percentile Rank