Amity Institute of Psychology and Allied Sciences

DATA
(FREQUENCY DISTRIBUTION)
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• Data (Score) Data

Ungrouped Grouped
Ungrouped Data -
This kind of data means –1) Raw Scores ,2) Independent Scores ,
3) these kind of Data have their own independent
identity, eg . 20,32,11,50 etc.
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DATA
Grouped Data - This kind of data means , that when data or Scores are
represented through some group or classification or class Interval they are
known as Grouped Data eg . 10 – 15 , 20 – 24 , 31-35, 45-50 .
Frequency Distribution :

Frequency distribution
Class interval

Tally Marks

Frequency
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Frequency Distribution ( Class Interval)

• when raw scores are distributed or represented with a particular class or
range of scores .For eg 10-14 , 15- 19, 20-24 etc ., it is known as class
Interval .
a)Types of Class Interval –

Class
Interval

Inclusive Exclusive
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Frequency Distribution ( Class Interval)--

• Inclusive Class Interval – When both the Upper limit and Lower limit of the
Class Interval are included in that particular class Interval , this type of Class
Interval is Known as Inclusive Class Interval eg .
35-39 here 20,25,30 and 35 are lower limit of each class Interval
30-34 and 24, 29,34 and 39 are upper limit of each class Interval .
25-29
20-24
Inclusive means –TO Include
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Frequency Distribution ( Class Interval )

• Exclusive Class Interval means when the Lower limit of the class Interval is included in that
particular class interval but the Upper limit of the class interval is excluded ( not included ) and
it becomes the lower limit of the next class Interval eg.
35-40 Here it can be seen that 20,25,30 and 35 are the lower limit
30-35 of each class interval and the Upper limit (25,30,35 ) are
25-30 repeated and are considered as Lower limit of next class
20-25 Interval .
While making Frequency Distribution for Exclusive Class Interval , scores which are
considered in class interval will be (20-24only and 25 will be excluded and it will become Lower
limit of next Class interval .
Exclusive – TO Exclude
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Frequency Distribution (class Interval)

Length Of the Class Interval – It means how many scores are lying in that particular Class
Interval eg. 20-24 (here 5 scores( 20,21,22,23,and 24) are there in this class interval.
It means the length of this class Interval is 5.
This Class Interval is Inclusive type of class interval where both lower limit and Upper limit is
included .
In Exclusive Type of Class Interval , it will be 20-25 , 25-30 and so on .
Here also Length of Class Interval will also be 5 (20,21,22,23,and 24 ) 25 is not considered as it
is Upper limit and in Exclusive type Upper limit is excluded and it becomes lower limit of next
class interval .
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Frequency Distribution ( Class Interval)

Length of Class Interval can be -------
2,3,4,5, 10,15,20,25 and so on .
As the length of class interval can be considered on the basis of Raw Scores
available to make Frequency Distribution .
• For eg in Raw scores till 50 to 60 ,we should make Class Interval with length
of 4, 5 will be best but 10 can also be considered .
• If we have Raw Scores -25 , 30 or 40 ,we can take length of -2,3 or 4 .
• In case we have Raw Scores around 60 or more (100 or
more ), length of 10 , 15 ,20 etc can be used .
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Frequency Distribution ( Tally Marks)

• Frequency Distribution ( Tally Marks)Tally Marks are used to
indicate number of scores that lie or fall in each class interval .
• Tally Marks are represented with a slanting line ( / ).
• If we want to represent 3 Scores than slanting line will be -///, so
it is clear that 1 slanting line is equal to 1 Score .
eg. //// = 4 scores , //// = 5 scores and //// / = 6 Scores ,
//// //// = 10 Scores .

• This way Tally Marks or Tallies are made .

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Frequency Distribution (Frequency-f)

• When Tallies are converted into Scores or numbers eg ////
- 4, it is known as Frequency .
Total Scores that lie in each Class Interval , when denoted
through numbers it is said to be frequency .
When all class intervals ‘ frequency are done , than all need
to be added.
Total Scores (frequency) of all class intervals when added ,
the final value is said to be N ( Total N).
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Format of Frequency Distribution

Class Interval Tallies f (frequency)
195 - 200 / 1
190 – 195 // 2
185 – 190 //// 4
180 – 185 //// 5

N = 12
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Steps Of Frequency Distribution

• (1) First we need to have Raw Scores or Ungrouped scores .
• (2) Now have to find out lowest score and the Highest Score
from the given Raw Scores.
• (3) We have to decide the Length of the Class Interval ,if it is
not told as per the Raw Scores.
• (4) Now start making class Interval from the lowest score eg
35 – 40 35 – 39 25 – 30 25 - 29
30 - 35 30 – 34 30 – 35 30 - 34
25 - 30 25 – 29 35 - 40 35 - 39
 Steps Of Frequency Distribution
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• (5) After Class Interval is made , than we have to make

Tallies eg

Inclusive Exclusive
Class Tallies f
Class Tallies f
Interval (frequenc
Interval (frequency)
(CI) y)
(CI)
35 - 39 ///
35 - 40 ///
30 - 34 //
30 - 35 //
25 – 29 //// //
25 - 30 //// //
N=
N=
 Steps Of Frequency Distribution
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• (6) After Tallies are made we now need to convert them

into numbers for Frequency eg .
Inclusive Exclusive
Class Tallies f Class Tallies f (frequency)
Interval ( CI (frequency) Interval (CI)
) 35 - 40 /// 3
35 - 39 /// 3
30 - 35 // 2
30 - 34 // 2
25 - 30 //// // 7
25 - 29 //// // 7
N = 12
N =12
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Problem of Frequency Distribution

• Tabulate the following 25 scores into a
frequency distribution using 60 70 80

an appropriate interval – 67 72 81

72 ,75, 77, 67 ,73, 81, 68, 65 , 86 ,73,67,82, 68 75 86

65 77 82
76,76,70,83, 71,63 67 73 83

72,72,61,67,84 , 69, 64. 63 73 84

61 76
67 76
69 70
OR
64 71
Lowest score -61 72
72
Highest Score -86
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Ways to choose scores for class interval

72, 75, 77,67,72,81,
68,65,86,73,67,82,76,76,70,83,71,63,72,72,61,67,84,69,64
While putting score in class interval either cut the score or put circle eg.
76 Or 82
When we have to make class interval with
60 70 80
Different length eg
67 72 81
76
68 75 86

65 77 82

67 72
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Problem : Frequency Distribution

Scores
Frequency
Distribution
60 70 80
Class Tallies f
67 72 81
Interval ( (frequenc
68 75 82 CL ) y)
65 77 83 85 - 89 / 1
67 72 84
80 - 84 //// 4
63 73 86
61 76 75 - 79 //// 4
67 76 70 - 74 //// // 7
69 70
65 - 69 //// / 6
64 71
72 60 – 64 /// 33
72
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Make a Frequency distribution with a class interval of 3
30 40 50
30 47 52 30,33,37,52,35,36,54,53,36,
33 46 54 34,52,38,58,57,53,51,54,
37 44 53
35 45 52
55,39,39,53,38,47,46,50,39,
36 41 58 44,45,52,51,41,40,39,48,43,
36 40 57 42,49,46,40,41
34 48 53
38 43 51
39 42 54
39 49 55
38 46 53
39 40 50
39 41 52
51