Organising and Condensing data

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Process of arranging and grouping of data in some orderly from is called organisation of data. To make the collection of data meaningful it is arranged in an orderly or sequence form. Data can be arranged in two forms:

Showing image of data can be arranged in two forms

Data Can Be Arranged in Two Forms

Showing image of data can be arranged in two forms

Arrays:

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Two Types of Arrays

Showing image of two types of arrays

Simply array:

  • It is the arrangement of data in ascending or descending order.

  • For ex. Ascending and descending array of the marks obtained by 5 students in a class.

Ascending and Descending Array
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Ascending order

Descending order

20

89

25

45

25

25

45

25

89

20

Frequency array:

  • It is a series formed on the basis of frequency with which each item is repeated in a series.

  • Main steps in constructing frequency array are:

    Steps of constructing frequency array

    Main Steps in Constructing Frequency Array

    Steps of constructing frequency array

  • For ex. Frequency array of marks obtained by 5 students.

Frequency Array of Marks Obtained by 5 Students
Showing image of example of frequency array of marks obtained by 5 students

Marks

Tally Sheet

Frequency

20

/

1

25

//

2

45

/

1

89

/

1

Total Frequency

5

Frequency Distribution:

Important concept for constructing frequency distribution.

Concepts of Frequency Distribution
Concepts of frequency distribution class, limts, intervals, frequency

Class

Class Limits

Class Interval (I)

Class Frequency

Mid-Point/Mid-Value (MV)

Class is a group of magnitudes having two ends called class limits.

Every class has two boundaries or limits called lower limit and upper limit.

Difference of two limits of a class is called interval.

Total number of items falling in a class that is having the value within and is class frequency.

Average value of two limits of a class. It fall just in the middle of a class.

Ex. In class 20-25, 25-30 etc. or 20-24, 25-29 etc.

Ex. In class (20-25)

Ex. In class (20-30)

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Construction of frequency distribution:

Showing iamge of construction of frequency distribution

Construction of Frequency Distribution

Showing iamge of construction of frequency distribution

Exclusive:

  • One of the class limits is excluded while making a tally sheet.

  • Any item having the value equal to the upper limit of a class is counted in the next class.

  • Ex. In a class of (20-25) all items having the value of 20 and more but less than 25 will be counted in this class.

Inclusive:

  • Lower limit of next class is increased by one over the upper limit of previous class.

  • Both item have value equal to lower and upper limit of a class are counted or included in the same class.

  • Ex. class (40-44) both 40 and 44 will be included.

Open end classes:

  • At least one of its ends open.

  • You will observe that either lower limit of first class or upper limit of class or both are not given in such series.

  • Ex. Class Below-35, 35-40, 40-45, 45 and above

Unequal classes:

  • Width of different classes need not be the same.

  • Ex. Class (30-35),(35-40),(40-50)

Cumulative:

  • Taking successive totals of given frequencies and total can be done two ways:

  • From above (Less-than cumulative frequency distribution): Total numbers of observations having less than a particular value of the variable.

  • From below (More than cumulative frequency distribution): Total number of observations having more than a particular value of the variable.