**Measure of Central Tendency:** It is a single value or figure that represents the entire set of data. It is a value to which most of the observations are closer.

## Meaning of Arithmetic Mean:

Arithmetic Mean is defined as “**the sum of the values of all observations divided by the number of observations”**. It is also known as ‘Mean’ or ‘Average’ by the common man. It is generally denoted by .

### Types of Arithmetic Mean

- Simple arithmetic mean
- Weighted arithmetic mean

### Objectives of Averages:

(1) To Present a Brief Picture of Data

- Averages summarises data into a single figure, which makes it easier to understand and remember.

(2) To Make Comparison Easier

- Averages are very helpful for making comparative studies as they reduce the bulky statistical data to a single figure.

(3) To Help in Decision-making

- Most of the decisions in research or planning are based on the average value of certain variables.

(4) To Help in Formulation of Policy

- It is very useful in policy formulation.
- For example: For the removal of poverty from India, government takes into consideration per capita income.

### Merits and Demerits of Arithmetic Mean

**(a) Following Are Some of the Merits of Arithmetic Mean:**

(1) Easy to Compute

- Its calculation is very easy because it requires knowledge of only simple mathematics i.e. addition, multiplication and division of numbers.

(2) Simple to Understand

- It is also simple to understand the meaning of arithmetic mean i.e., the value per unit or cost per unit, etc.

(3) Based on All Items

- It takes into consideration all the values of data.
- It is considered to be more representative of the distribution.

(4) Rigidly Defined

- Its value is always definite because it is rigidly defined.

(5) Good Basis of Comparison

- It provides a sound basis of comparison of two or more group of data.

(6) Algebraic Treatment

- It is capable of further algebraic treatment. So, it is widely used in advance statistical analysis.

**Following Are Some of the Demerits of Arithmetic Mean:**

(1) Complete Data is Required

- It cannot be computed unless all the items of a series are available.

(2) Affected by Extreme Values

- Since arithmetic average is calculated from all the items of a series, it can be unduly affected by extreme values i.e. very small or very large items.

(3) Absurd Result

- Sometimes arithmetic mean gives absurd results. For example, if a teacher says that average number of students in a class is 28.75, it sounds illogical.

(4) Calculation of Mean by Observation Not Possible

- Arithmetic mean cannot be computed by simply observing the series like median or mode.

(5) No Graphic Representation

- Arithmetic Mean cannot be represented or depicted on graph paper.

(6) Not Possible in Case of Open Ended Frequency Distribution

- In case of open ended class frequency distribution, it is not possible to compute arithmetic mean without making assumption about the class size.

(7) Not Possible in Case of Qualitative Characteristics

- It cannot be computed for a qualitative data; like data on intelligence, honesty, smoking habit, etc.

### What Are the Essentials of a Good Average?

(1) Easy to Understand

- It should be easy to understand so that a layman can use it.

(2) Easy to Compute

- It should be easy to compute.
- Its calculation should not involve mathematical complexities.

(3) Based on All Observations

- Average should be calculated by taking into consideration each and every item of the series.

(4) Rigidly Defined

- It should have a definite and fixed value irrespective of method of calculations.

(5) Capable of Further Algebraic Treatment

- It should be capable of further algebraic treatment so that it can be used advance analysis.

(6) Not Affected Much by Extreme Values

- The value of an average should not be affected much by extreme values.
- One or two very small or very large values, should not affect the value of the average significantly.

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