CONTENTS UNDER : Classification of data:

frequency distribution*Introduction

*Classification of data* Objectives of classification

*Methods of classification Variable*Way to classify numerical data or raw data

*General rules for constructing a grouped frequency distribution*Conclusion

CLASSIFICATION OF DATA: FREQUENCY

DISTRIBUTION

INTRODUCTIONAfter the data have been collected, the next step is to present the data in some orderly and logical form so that their essential features may

become explicit. The need for proper presentation of data arises because the mass of collected data in their

raw form is often so volumes, unintelligible and uninteresting that it starts at the face of the reader.

CLASSIFICATION OF DATA

Classification is the process of arranging the data into different groups or classes according to some

common characteristics.“Classification is the process of arranging things in

groups according to their resemblances and affinities”.

-CONNOR“Classification is the grouping of related facts into

classes” -SPURR AND SMITH

OBJECTIVES OF CLASSIFICATION

*To condense the mass of data in such a way that their similarities and dissimilarities

become very clear.*To facilitate comparisons, i.e., to make the

data comparable.*To point out the most important features of

the data at a glance.*To present the data in a brief form.

*To make data attractive and effective.

METHODS OF CLASSIFICATION

Classification

Geographical Chronological Qualitative Quantitative

1.GEOGRAPHICAL CLASSIFICATION

In geographical classification, data are classified on the basis of geographical or locational differences between the

various items. For example:-No. of firms producing bicycles in 2001

STATE NO. OF FIRMSPunjab 30Haryana 20U.P. 25

2.CHRONOLOGICAL CLASSIFICATION

When the data are classified on the basis of time, it is known as chronological

classification. For example:-Population of India (1951-1991)

YEAR POPULATION (IN CRORES)

1951 36.11961 43.91971 54.81981 68.41991 84.4

3.QUALITATIVE CLASSIFICATION

In this type of classification, data are classified on the basis of some attribute or quality such as sex, literacy,

religion, etc.

Qualitative Classification

Simple Classification Manifold Classification

4.QUANTITATIVE CLASSIFICATION

When data are classified on the basis of some characteristics which is capable of direct quantitative measurement such

as height, weight, income, marks, etc., it is called quantitative classification. For

example:-Students may be classified according to

weight in table

WEIGHT(IN IBS) NO. OF STUDENTS70-80 4080-90 5090-100 150100-110 250

VARIABLEThe characteristic, which is capable of

direct quantitative measurement is called a variable or variate .

Variable

Discrete Continuous variable

variable

WAY TO CLASSIFY NUMERICAL DATA

OR RAW DATANumerical data or Raw data

Ordered array or FrequencyIndividual series distribution Discrete series Continuous series

GENERAL RULES FOR CONSTRUCTING A

GROUPED FREQUENCY

DISTRIBUTION1.Selection of number of classes

2.Size (or width) of class intervals 3.Selection of class limits

4.Kinds of continuous series

1.SELECTION OF NUMBER OF CLASSESThere are no hard and fast rules about the selection of

number of classes. It depends on number of factors such as:-

*The number of items to be classified *The magnitude of the class interval

*The accuracy desired*The ease of calculation for further processing of data

*size of class intervalsProf. H.A.Sturge gave a formula by which the number of

class interval can be ascertained. The formula isk =1+3.322log N

(Here k= number of class intervals, N=number of observations)

2.SIZE (OR WIDTH) OF CLASS INTERVALS The choice of class interval depends on the number of classes for a given distribution and the size of the data. Prof. Sturge has

given the following formula for determining the size of class intervals:-

Size of class interval:i=Largest value-Smallest value

1+3.322logN

3.SELECTION OF CLASS LIMITS

Class limits should be selected in such a way that-

*The mid values of classes coincide or come very close to the point of

concentration in the data.*The overlapping of classes is avoided.

*The class limits must be stated precisely enough so that there will be no confusion

as to what they include.

4.KINDS OF CONTINUOUS SERIES

There is another important problem relevant to constructing a frequency distribution. These

relate to kinds of grouped or continuous series to be formed. The following are the important

kinds of continuous series:-(a)Exclusive series(b)Inclusive series

(c)Open ended series(d)Mid-value series

(e)Cumulative frequency series

(A)EXCLUSIVE SERIES

Exclusive series is that series in which every class interval excludes items

corresponding to its upper limit. In this series, the upper limit of one class

interval is the lower limit of next class interval.

Exclusive series MARKS FREQUENCY10-15 415-20 520-25 8TOTAL 17

(B)INCLUSIVE SERIES

An inclusive series is that series which includes all items upto its upper limits,

the upper limit of class interval does not repeat itself as a lower limit of the next

class interval.Inclusive series MARKS FREQUENCY

10-14 515-19 420-24 8TOTAL 17

(C)OPEN ENDED SERIESIn some series, the lower class limit of the first class interval and the upper

limit of the last class interval are missing. Instead, less than or below and

more than or above is specified.Open ended series MARKS FREQUENCY

LESS THAN 5 15-10 310-15 415-20 620 AND ABOVE 1

(D)MID-VALUE SERIES

Frequency series containing mid-values is that series in which we have only mid-values of the class intervals and the

corresponding frequencies.Mid-value series

MID-VALUE FREQUENCY5 315 825 535 7

(E)CUMULATIVE FREQUENCY SERIES

Cumulative frequency series is that series in which the frequencies are added corresponding to each class

interval in the distribution. The frequencies than become cumulative

frequency.Cumulative frequency series MARKS FREQUENCY CUMULATIVE

FREQUENCIES5-10 3 310-15 8 8+3=1115-20 9 11+9=20

CONCLUSIONAt last conclusion of classification of data

is, it makes data comparative, attractive , effective and very simple

. Classification clearly shows differences or comparison of figures .

One important point is that it makes data ready for further statistical process.