Organizing The Data

Statistics

Organizing the Data

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11420215

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