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.