# Analysis of Data: Meaning of Central Tendency, Purpose and Functions of Averages (For CBSE, ICSE, IAS, NET, NRA 2022)

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Economic data are usually studied with the help of statistical methods. Science of statistics is a method of collection, classification and tabulation of numerical facts, which help in explanation, description and comparison of phenomena.

## Meaning of Central Tendency

• After the data have been collected, organized and presented they need to be analyzed. 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. In statistics we deal with certain problems, which are largely affected by multiplicity of causes. Whatever conclusions we draw are based on combined effect of the various causes and it is very difficult to trace out impact of all such causes separately. However, the first step in data analysis is to ascertain representative values from the raw data. It is known as average or measure of 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.
• 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

There are various measures of central tendency. Arithmetic mean is one of them Arithmetic mean is obtained by dividing the sum of the items by the number of items mathematically speaking.

X̄ = Σx/N

where, x = item

Σx = sum of the item

N = Number of items and

X = Arithmetic mean

## Calculation of Arithmetic Mean in Different 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:

X̄ = Σdx/N

Here A is assumed mean, dx is deviating x from assumed mean and N is number of items.

### Discrete Series

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

#### Direct Method

X̄ = Σfdx/N

where N = Sum of frequencies

X̄ = A + Σfdx/N

### Continuous Series

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

X̄ = Σfdx/N

#### Shortcut Method Without Step Deviation

x = mid value of a class

X̄ = A + Σfdx/N

Shortcut method with step deviation

X̄ = A + Σfdx ⚹ c/N

Here c = common factor

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