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 the observations divided by the number of observations. It is also known as the mean or average. It is generally denoted by xˉ or A.
Types of Arithmetic Mean
- Simple arithmetic mean
- Weighted arithmetic mean
Objectives of Average
(1) To present a brief picture of data
- The average summarises the data into a single figure, which makes it easier to understand and remember.
(2) To make comparisons easier
- Averages are very helpful for making comparative studies as they reduce the bulky statistical data into 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 policies
- It is very useful in policy formulation.
- For example, for the removal of poverty from India, the government takes the per capita income into consideration.
Merits and Demerits of Arithmetic Mean
(a) The following are some of the merits of using arithmetic mean:
(1) Easy to compute
- Its calculation is very easy because it just requires the knowledge of basic mathematics, i.e., addition, multiplication, and division of numbers.
(2) Simple to understand
- It is simple to understand the meaning of arithmetic mean i.e., the value per unit or the cost per unit.
(3) Based on all items
- It takes all the values of the data into consideration.
- 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 basis of comparison of two or more groups of data.
(6) Algebraic treatment
- It is capable of further algebraic treatment. So, it is widely used in advanced statistical analyses.
The 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 the arithmetic average is calculated from all the items of a series, it can be unduly affected by the extreme values, i.e., very small or very large ones.
(3) Absurd results
- Sometimes, the arithmetic mean gives absurd results. For example, if a teacher says that the average number of students in a class is 28.75, it sounds illogical.
(4) Calculation of mean by observation is not possible
- The arithmetic mean cannot be calculated by simply observing the series like median or mode.
(5) No graphic representation
- The arithmetic mean cannot be represented or depicted on a graph paper.
(6) Not possible in case of an open-ended frequency distribution
- In case of an open-ended class frequency distribution, it is not possible to compute the arithmetic mean without making an assumption about the class size.
(7) Not possible in case of qualitative characteristics
- It cannot be computed for qualitative data, like data on intelligence, honesty, smoking habits, 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
- The 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 the method of calculations.
(5) Capable of further algebraic treatment
- It should be capable of further algebraic treatment so that it can be used for advanced analysis.
(6) Not affected much by extreme values
- The value of the average should not be affected much by extreme values.
- One or two very small or large values should not affect the value of the average significantly.