Economics: Analysis of Data: Meaning, Central Tendency, Purpose and Functions of Averages

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Meaning

Analysis of data is a technique through which significant fact from the numerical data are extracted. One of the most important objects of statistical analysis is to get one single value that describe the characteristics of the whole data.

Central Tendency

  • Raw data are first edited and then converted into frequency distribution. One of the basic purposes of descriptive statistics is to find out a most representative value or figure from the data. This representative figure is called average or mean. This is the value or single figure, which is typical to all. This is also known as measure of central tendency. Thus, averages are the descriptive statistics, which measure the tendency called central tendency.

  • Tendency of data to cluster towards the central location or value is called central tendency.

Purpose and Functions of Averages

  • To convert the collected information and raw data in brief

  • To facilitate comparison between two or more groups

  • To present a representative value from raw data

  • To facilitate future policy and programme.

Arithmetic Mean as a Measure of Central Tendency

Arithmetic mean in common language is popularly known as average. Arithmetic mean is obtained by dividing the sum of the items by the number of items. Formula,

=

Where, x = item

= sum of the item

N = Number of items and

X = Arithmetic mean

Calculation of Arithmetic Mean in Different Types of Series

Types of Series

Types of Series

Individual Series

Above formula for calculation of arithmetic mean or mean is valid under all circumstances. However, if shortcut method is to be used for complexed data, above formula is modified as follows:

  • Direct Method Formula, =

  • Shortcut Method Formula, =A +

Discrete Series

For ascertainment of arithmetic mean in discrete series following formulae can be used

  • Direct method, =

  • Shortcut method, =A +

Continuous Series

Following three methods are used for ascertainment of arithmetic mean in a continuous series

  • Direct method, =

  • Shortcut method, =A + , where x = mid value of class

  • Shortcut method with step deviation, =A +

Precautions of Using Arithmetic Mean

  • It is important to note that arithmetic mean is a theoretical value, which may not be represented by actual fact.

  • Arithmetic mean cannot be qualitative data such as honesty, bravery, loyalty and beauty etc.

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