UNIT-III

CLASSIFICATION

CLASSIFICATION: �

Meaning and objectives of classification – types of classification – formation of a Discrete and continuous Frequency Distribution – Histogram – Frequency Polygon – Limitations of Diagrams and Graphs.

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Meaning of Classification: �

• It is the process of arranging data into homogeneous (similar) groups or classes according to resemblances and similarities.
• Raw data cannot be easily understood and it is not fit for further analysis and interpretation.
• This arrangement of data helps users in comparison and analysis. For example, the Population of town can be grouped according to Gender, age, marital status etc.

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Definition: �

• The process of grouping a large number of individual facts or observation on the basis of similarity among the items is called Classification.

-Stockton and Clark

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• Classification is the process of arranging data into sequences and groups according to their common characteristics or separating them into different but related parts.

-Secrist

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Chief characteristics of classification

• All the facts are classified into homogenous groups by the process of classification
• The basis of classification is unity in diversity.
• Classification may be according to either similarities or dissimilarities.
• Classification may be either real or imaginary.
• It should be flexible to accommodate adjustments.

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Objectives of Classification: �

• To condense the mass of data
• To present the facts in a simple form
• To bring out clearly the points of similarity and dissimilarity
• To facilitate comparison
• To bring out the relation among the data
• To prepare data for tabulation
• To facilitate statistical treatment of the data.
• To facilitate easy interpretation
• To eliminate unnecessary details.

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�Requirements of a good classification / Rules of classification: �

The classification of data is a pre-requisite for the statistical analysis. Thus, a good classification should fulfil the following requirements:

• Exactness
• Mutually exclusive
• Stability
• Flexibility
• Suitability
• Homogeneity
• Mathematical Accuracy

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Frequency Distribution

• A frequency distribution or frequency table is a table which the data are grouped into classes and number of cases in each class are recorded.
• The number in each class is referred to as “frequency”.
• There are individual observations, discrete frequency distribution and continuous frequency distribution.

Individual Observation

• Individual series refers to that series in which items are listed in single, i.e. each item is given a separate value of the measurement such as height, weight etc., are also called simple frequency distribution.
• Example:

The following are the marks obtained in Statistics:

40, 50, 55, 78, 58, 60, 73, 35, 43, 48, 31, 77, 55, 45, 37.

Discrete frequency distribution

• In this distribution, we have to count the number of times a particular value is repeated. This is called the frequency of that class.
• For example: the following are the marks in statistics secured by 15 students in a class.

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Steps in the construction of discrete frequency distribution

• Prepare three columns – one for the variable, another for bars and third for the frequency corresponding to the variables.
• Arrange the given values from the lowest to the highest in the first column.
• In the second column, put a bar (vertical line) opposite to the particular value that it is repeated.
• Count the bars and place it opposite to the value of the variable in the third column.

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For Example

• Following are the marks obtained by 25 students (out of 10). Make a discrete frequency distribution.

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Solution

The following are the discrete frequency distribution of 25 students :

Class work Problem:

• Following are the marks obtained by 30 students. Make a discrete frequency distribution:

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The following are the discrete frequency distribution of 30 students:

Home Work

• the following are the marks obtained by 40 students. Make a discrete frequency distribution with tally bars.

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Continuous frequency distribution

• When items are arranged in groups or classes, because they are not exactly measurable, they form continuous series.
• A collection of items, which cannot be exactly measured, but placed within certain limits, is called continuous series.
• Class – Limits: are the lowest and the highest values that can be included in the class.
• For example: take the class 30-40. the lowest limit is 30 and the highest limit is 40.

Methods of Class-Interval

• Exclusive method
• Inclusive method

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Exclusive method

• Under this method, the upper limit of one class-interval is the lower limit of the next class.
• For Example :

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Inclusive Method (Non-overlapping)

• In this method the upper limit of one class is included in that class itself, for example:

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• Marks scored by 30 students are given below:

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• Arrange in Ascending order
• Arrange in descending order
• Convert the marks into a continuous series of a class- interval of 10.

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PROBLEM:

Solution

• (A) Marks arranged in Ascending order:

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• (B) Marks arranged in Descending order:

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• (C) Formation of continuous series:

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• The following are the Continuous class frequency of 30 students:

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Home work

• In a survey of 30 workers in a factory, the amount of wage earned per worker was recorded and the following data were obtained:

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Cumulative Frequency Distribution

• The cumulative frequencies are derived by the cumulation of the frequencies of successive values. Cumulative frequency of a given variable or class represents the total frequency of all previous variables including the variable or the class.

There are two methods of expressing the cumulative frequencies. They are:

• More than cumulative frequency distribution
• Less than cumulative frequency distribution

Less than Cumulative Frequency Distribution

• For any value of the variable or class is obtained by adding successively the frequencies of all the previous variables including the variable or lass against which it is written.
• The cumulation is started from the lowest size to the highest size.

1. Calculate less than cf for the following data:

Solution:

Classwork problem

• Find less than cumulative frequency distribution:

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Solution:

• Less than C.F.D

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Homework problem

1. Make a frequency distribution with class intervals of 10.
2. Also prepare less than cumulative frequency distribution.
3. Also prepare more than cumulative frequency distribution.

More than Cumulative Frequency Distribution

• It is obtained by finding the cumulation total of frequencies starting from the highest to the lowest variable or class.

1. Calculate More than cf for the following data:

Solution

4. Find more than cumulative frequency distribution:

Solution

DIAGRAMMATIC PRESENTATION

• A diagram is a visual form for presentation of statistical data.
• Diagram refers to the various types of devices such as bars, circles, maps, pictorials, cartograms, etc. these devices can take many attractive forms.
• An ordinary man can understand pictures more easily than figures.

ADVANTAGES OF DIAGRAM

• They are attractive and impressive
• It helps to save time and labour.
• They have universal applicability.
• They make data simple.
• It helps in comparison.
• They provide more information.

LIMITATIONS OF A DIAGRAM

• Diagrams cannot be analysed further
• It shows only approximate values.
• It exposes only limited facts. All details cannot be presented diagrammatically.
• It is a supplement to the tabular presentation but not an alternative to it.
• Minute readings cannot be made.
• Diagrams are drawn when comparison needed, otherwise, they are of little in use.

RULES FOR MAKING A DIAGRAM

• HEADING - Every diagram must have suitable title. The title, in bold letters, conveys the main facts depicted by the diagram.
• SIZE – It should be neither be too big nor too small. It must watch with the size of the paper. It should be in the middle of the paper.
• LENGTH AND BREADTH – An appropriate proportion should be maintained between length and breadth.

• SELECTION OF APPROPRIATE DIAGRAM – All types of diagrams are not suitable for all types of data. A wrong selection may distort the true characteristics of the phenomenon to be presented and might lead to very wrong and misleading interpretation.
• CLEANLINESS - Diagrams must be as simple as possible. Further they must be quite neat and clean. They should also be descent to look at.
• INDEX - Every diagram or graph must be accompanied by an index. This illustrates different types of lines, shades or colors used in the diagram.

TYPES OF DIAGRAM

• One dimensional diagram ( Line and Bar )
• Two-dimensional diagram (rectangle, square etc )
• Three-dimensional diagram ( cube, sphere etc )
• Pictogram
• Cartogram

ONE-DIMENSIONAL DIAGRAM

• LINE DIAGRAM –PROBLEM
• The following data show the number of child birth to 125 females in a hospital in one year . Draw a suitable diagram.

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Home work Problem

• The following data show the number of accidents sustained by 100 drivers of a company in a particular year. Draw a suitable diagram.

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BAR DIAGRAM

• The following data show the seasonal fluctuations in production of wheat during 2010. Draw (A) Horizontal Bar diagram and (B) Vertical Bar diagram.

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(A) Horizontal Bar Diagram

• The number of students in a university is given below. Represent the data by a suitable diagram.

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ANGULAR OR PIE DIAGRAM

• The following table shows the area in millions of square kilometres of the oceans of the world:

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• Draw a pie diagram to represent the data.

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Solution

Classwork problem

• Represent the following data by pie diagram.

Solution