MEAN - DEFINITION AND CALCULATION
INTRODUCTION
Mean, median and mode all three are Central Tendency or Averages. The Arithmetic mean lies under Mathematical Average and the other two Median and Mode are types of Positional Averages. A measure of central tendency is a typical value around which the figures congregate”. The value of central tendency or average always lies between the minimum and maximum values.
MEAN
Arithmetic mean is defined as the quantity obtained by adding together all the given observations and by dividing this total by the number of items.
Mean or Arithmetic mean = sum of values of observations/ number of observations
CALCULATION
For individual observations
It is done when the observations are not in frequencies, so the calculation of mean is very simple.
Add all the values and divide it by number of values.
- Direct Method :
FORMULA :
Where,
x͞ = arithmetic mean
∑x = sum of variables
N = Number of observations
Shortcut Method
Where,
x͞ = Arithmetic mean
A= Assumed mean
∑d= Sum of the deviations
N= Number of items
For discrete series
This method is used when values are given in frequencies.
In direct method, the values of variable are multiplied by their respective frequencies and the products obtained and totalled. this total is divided by the total number of frequencies.
ARITHMETIC MEAN = THE SUM OF PRODUCTS/ TOTAL FREQUENCY
1.Direct Method :
Where,
x͞ =Arithmetic mean
∑fx= the sum of products
∑f= total of frequency
2. Short-cut Method :
FORMULA :
Where,
x͞= Arithmetic mean
A= Assumed mean
∑fd= Sum of total deviations
∑f= Total frequency
For Continuous Series
This method is used when the value of each individual frequency distribution is unknown.
In direct method,
- First find out the mid value by adding the lower limit and upper limit of the class and dividing the total by two.
- Multiply the mid value of each class by the frequency of the class.
- Add all the products.
- Then divide sum of products by total frequency.
MEAN = SUM OF ARITHMETIC MEAN / TOTAL OF FREQUENCY
- Direct Method :
Where,
x͞= Arithmetic mean
∑fmid x= the sum of products
∑f = total of frequency
2. Shortcut Mean:
Where,
x͞= Arithmetic mean
A = Assumed mean
∑fd= Sum of total deviations
∑f= Total frequency
MERITS OF THE MEAN
- It is easy to understand
- It is easy to calculate
- Sampling fluctuations do not affect the value of mean.
- It is least affected by the fluctuation of sampling.
DEMERITS OF THE MEDIAN
- Mean value is very much influenced by very big or very small numbers.
- It is not positional like median and mode.
- Sometimes it may give false conclusion.
- Upward biased, means it give importance to bigger values.
- Never be determined by graphical location.
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