Presentation on�Presentation of the data�Presented by�Mr. Somnath D. Karande�Department of Statistics�Raje Ramrao Mahavidyalaya, Jath�Dist- Sangli �

• Presentation of data

• Classification:
• Raw data: In order to study a characteristic of any type, the 1^st phase is to collect the data. The unprocessed data are called as raw data.
• Classification of data:

After collecting and editing of data the first step towards a processing it is the classification. Classification is the process of separating the whole data into various classes according to similarity or dissimilarity of the character under consideration. i.e. In classification of data units having the common characteristic are placed in one class and in this manner the whole data are divided into number of classes.

e.g. student studying in a college can be classified according to their faculties like science, arts and commerce. Or they can be classified according to their grades obtained in the last examination or they can be classified according to their sex, religion etc.

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• Frequency distribution:

When we distributed data into classes, the numbers of observations belonging to each class is called as the class frequency. A tabular arrangement of data by class together with the corresponding class frequencies is called a frequency distribution or frequency table.

Frequency distribution is constructed in two ways as discrete (ungrouped) frequency distribution and continuous (grouped) frequency distribution.

1) Discrete frequency distribution:

(Ungrouped data)

When the variable is discrete and if it assumes only few values then it is possible to construct a frequency distribution by taking all possible values of the variable together with their repetitions (frequencies). This frequency distribution is called as discrete frequency distribution.

e.g.

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2) Continuous frequency distribution:

(Grouped data)

When the values of a variable are not few in number then data is divided into suitable number of classes or groups. Each group is in the form of class intervals and frequency distribution so constructed is known as continuous frequency distribution.

e.g.

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Various terms used in continuous frequency distribution

1) Class interval:

The observations which have common resemblance (Some similarities) are put into a group known as a class interval or simply class. 0-10, 10-20, 20-30 are class intervals i.e. classes.

2) Class limits:

The two numbers designating a class interval are called class limits. The lowest value is called lower limit and highest value is called upper limit.

e.g. In the class interval 10–15. 10 and 15 are class limits. Where 10 is a lower limit & 15 is a upper limit.

3) Open end class:

If for a class either the lower limit or the upper limit is not specified then this class is known as open end class.

Classes

Below 500

500-1000

Open end Class 1000-1500

Above 1500

4) Class boundaries:

Class boundaries are the number up to which the actual magnitude of observation in the class can be extended.

e.g.

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• Methods of Classification

There are two methods of classification

1) Inclusive method

2) Exclusive method

1) Inclusive method:

If upper limit of the classes are included in the same class then the classes are inclusive type classes.

e.g. If we are given the classes of marks of students of the type 0-9, 10-19, 20-29, 30-39 etc. In this case a student whose marks are 9 included in the 1^st class and a student whose marks are 19 included in the 2^nd class and so on. It can be observed that the upper limit of class is not same as the lower limit of succeeding class. Therefore a discontinuity is observed between the classes. Thus the meaning of the term inclusive is including the upper limit of the class.

2) Exclusive method:

If upper limits of the classes are excluded from the respective classes then the classes are exclusive type.

e.g. If we are given the classes of marks of students of the type 0-10, 10-20, 20-30, 30-40etc. In this case a student whose marks are 10 included in the 2^nd class but not in the 1^st class. A student whose marks are 20 included in the 3rd class but not in the 2^nd class and so on. It can be observed that the upper limit of class is same as the lower limit of succeeding class. Therefore the classes are observed to be continuous without any gap between the classes. Thus the meaning of the term exclusive is excluding the upper limit of the class.

• Cumulative frequency distribution

In many situations it is required to find the number of observations below or above a certain value. e.g. In case of a frequency distribution of income, the number of persons below poverty line or in case of frequency distribution of examination marks, number of student above 40 etc is required to be found. In such cases cumulative frequencies are very useful.

There are two types of cumulative frequencies

1) Less than type cumulative frequency

2) More than type cumulative frequency

1) Less than type cumulative frequency:

Less than type cumulative frequency of a class is the number of observations less than or equal to the upper limit of a corresponding class.

• Less than type cumulative frequency of class can be obtained by computing cumulative sum of frequencies from the lowest class to highest class.
• Less than type cumulative frequency is increasing in nature.

e.g.

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2) More than type cumulative frequency:

More than type cumulative frequency of a class is the number of observations more than or equal to the lower limit of the corresponding class.

• More than type cumulative frequency can be obtained by corresponding cumulative sum of frequencies from the highest class to lowest class.
• More than type cumulative frequency is decreasing in nature.

e.g.

• Relative frequency

• Tabulation

Tabulation is a systematic and logical representation of numerical data in rows and columns to facilitate comparison and statistical analysis.

• Part of table:

Generally, a table has following parts.

1. Table number
2. Title of the table
3. Head Note
4. Caption
5. Stub
6. Body of the table
7. Foot-Note
8. Source Note

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Following diagram shows the part of table,

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Table Number

Title

Head Note

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Foot-Note

Source Note

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1. Table number: Each table should be given a number for ready reference.
2. Title: Each table should be given a short, clear & precise title is to briefly describe i) The material of the table ii) The time of collection and iii) The area covered.
3. Head note: The purpose of head note is to state units and to qualify the Title.
4. Caption: Caption refers to the heading of the columns. If there are many columns, sub-headings should be given.
5. Stub: Stub refers to the heading of the rows. They are given at the extreme left.
6. Body: This is the main part of the table wherein data are given in numerical form.
7. Foot note: It is given at the foot of the table. Its purpose is to indicate i) Special features, if any ii) Special circumstances, if any.
8. Source note: If data are taken from some other sources it is to be mentioned in this note. All information such as name of the publication, year, table number etc. About the source should be given in the source note.

• Characteristics of good table:
• It should be suitable for a purpose.
• Clarity and completeness of table is necessary.
• Table should be of adequate size.
• Units of measurements should be specified.
• Logical arrangement of items.
• Totals and subtotals should be given.

• Types of table:
• Table may be broadly classified into categories,
• Simple & Complex table (According to construction)
• General purpose & Special purpose table (According to purpose)
• Original table and Derived table (According to originality)

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1) Simple & Complex table:

The distinction between simple and complex tables is based upon the number of characteristics studied. Only one characteristic is displayed in the simple table. As a result, this table is often known as a one-way table. While two or more attributes (characteristics) are displayed in a complex table.

e.g. Simple table

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e.g. Complex table

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2) General purpose & Special purpose table:

• General purpose table:

General purpose tables are often known as reference tables and they contain information that is intended for general use or reference.

• Special purpose table:

Special purpose tables are often known as summary or analytical tables and they contain information relevant to a certain topic.

3) Original table and derived table:

• Original table:

In this type table, data are presented in the same form as they are collected.

• Derived table:

Under this type of table, data are not presented in the form and manner as they are collected. Rather the data is first converted into ratios or percentage and then presented.

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Thank you