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Following are the four characteristics of arithmetic mean:

1. Its algebraic use is possible. 

2. Its calculation is simple. 

3. It keeps all the items in mind. 

4. It is the most popular medium for comparative study.

Following are the four characteristics of an ideal mean: 

• It should be defined clearly : The mean should be defined very clearly so that it has only one implication. 
• It should be simple to understand and simple to compute: The mean should be such that it is simple to understand and simple to compute.
• It should be based on all the values : An ideal mean should be based on all the values of the series. Without this, this mean will not represent the data-item series correctly. 
• It should be the least affected by extreme values (maximum/ minimum) : The extremely small and extremely large values of a data-items series should have the least effect on the mean.

Continuous series

Arithmetic Mean

Statistical means have a considerable use in practical life. With their help, systematic and complex data is presented in simple form. It represents the entirety. Two or more groups can be compared. It presents a basis in the process of other statistical analysis, and in determining future policies, these serve as a guide.

Statistical mean is such a representative value of the data series that highlights the key feature of the data series, and around which tendency of other data in the data range to concentrate is found. This is the most popular measure of central tendency. The reason for this is its simple calculation method.

Individual series

1. Arithmetic Mean 

2. Geometric Mean

Two types of means are related to place.

Four Types of mathematical means are there.

1. With the help of means, we can present complex data in a simple and concise form. 

2. Measures of central value , by reducing the volume of data to single figure, enable comparison to be made.

1. Variable mean 

2. Progressive mean 

3. Documented mean

Correct Answer is: (a) Median

Median(M) and Mode (Z)

(d) All of these

Correct Answer is: (c) Mode

(a) Arithmetic mean

(a) Arithmetic mean

Correct Answer is: (c) Zero

Correct Answer is: (b) 0

If the class magnitude is the same in the continuous category, and if the number of class-intervals is large, then the step-deviation method is used to further simplify the shortcut method.

Since among all statistical means, arithmetic mean is more simple and simple to calculate, it is more useful for study of economic and social problems. It is of extensive use in determining average production, average investment (cost), average income, average import-export, average bonus, etc. Despite effect of extreme values, unrepresentative nature, misleading results being its disadvantages, arithmetic mean can be considered to be the ideal mean.

Meaning of arithmetic mean : Arithmetic mean is the most popular and important means among mathematical means, which is generally used by the common man in routine life. The arithmetic mean of a series is the value which is obtained by dividing the sum of all the values of the series by the number of items present in it.

According to H.Secrist : “ Arithmetic mean is the amount secured by dividing the sum of values of the items in a series by their number.”

Thus, it is clear that the arithmetic mean is found in the sum of all the values of a general category, divided by the number of values.

For example: if the monthly income of 5 families is ? 2000, 3000, 4000, 5000 and ? 6000, then for finding out the arithmetic mean or average income of the families, the incomes of all these households is added together, which is Rs. 20000 and then total income will be divided by the total number of items which is 5, The average monthly income will be Rs. 4000, that is the arithmetic mean. 

Arithmetic mean is of two types:

1. Simple Arithmetic Mean 

2. Weighted Arithmetic Mean

Merits of Arithmetic Mean : 

Following are the merits of arithmetic mean.

• Easy to compute and understand : It is the simplest average to understand and easiest to compute. A layman can also understand it easily. 
• Based on all items of the series : It takes into consideration every item in the series in computation. Thus, it is a good representative value.
•  Definitiveness : It is defined by a rigid mathematical formula with the result that everyone who computes the average gets the same answer. 
• Stability : In comparison to other averages, mean is quite stable. It does not vary too much when repeated samples are taken from one and the same population, at least not as much as some other kind of statistical descriptions do. 
• Suitable for algebraic treatment : Being determined by a rigid formula, it lends itself to subsequent algebraic treatment better than the median or mode. 
• No need for arranging data : It is not necessary to arrange the values in an array form. 
• Comparative Study : With its help, two series can be easily compared.
• Calculation of Unknown Values : If among the arithmetic mean, number of items and sum of items, any one is unknown, then it can be calculated using the two known values.

Following are the demerits of arithmetic mean:

• Effect of extreme value : The value of arithmetic mean depends upon each and every item of the series. Therefore, extreme items, i.e. very small and very large items affect the average figure disproportionately. 
• Unrealistic : Sometimes it may represent such figure which seems to be unrealistic. 
• Graphical representation is not possible : It cannot be located by graphic method. 
• Calculation difficulties : In comparison to positional averages, calculation of arithmetic mean is more difficult because

1. It cannot be located by mere inspection, while some other averages can be located by mere inspection. 

2. It cannot be determined even if one of the values is not known because it takes into consideration every item in the series in computation. 

3. It is not suitable for qualitative facts.

• Misleading conclusions : Sometimes it gives misleading and inconsistent conclusions. 
• Not suitable in the study of rate, ratio and percentage : It is not suitable for the study of rate, ratio and percentage.