Properties of Arithmetic Mean

Following are some of the important properties of arithmetic mean, which are elaborated with the help of simple problems.

Problem: A researcher conducted a research and got the observations: 50, 60, 65, 75, and 80. Using these observations explain the different properties of mean.

  • The sum of the deviations of the observations from their mean is always zero.

 

 

In the above table we first calculated the mean (mean = 66) and then calculated the difference of each observation from the mean. As shown in the table the sum of deviation of these observations from mean is always zero.

  • The sum of squared deviation of the observations from their mean is minimum

 

 

After taking square of deviations of the observations from their mean and adding those up it is found that sum of squared deviation of the observations from their mean is 570 which is less than 1850. We can also try other values such as 60, 65, 75 etc but sum of squared deviation of the observations from their mean will always be minimum.

 

  • If we have one variable x and we transform this variable into y (by multiplying it with constant number and adding another constant number to it). The mean of this new variable y can be obtained by the same transformation of x bar.

 

 

It is evident from the above table that the mean (y bar) of transformed variable y can be calculated either by dividing the sum of total observations by total number or by transforming the x bar by multiplying it with 2 and adding 3 to it. This transformation is called a linear transformation.

 

  • Mean of constant number is the constant

 

 

For example we have six constant observations e.g. 8, 8, 8, 8, 8, and 8. Now mean can be calculated by using the formula:

 

Page: 1 2

kasi

View Comments

Recent Posts

Porter’s Five Forces of Microsoft

Microsoft Corporation also known as MS is one of the biggest multinational technology-based company in…

2 years ago

Porter’s 5 Forces Analysis of Fast Food Industry

The article is based upon in-depth analysis of Fast Food Industry of Australian Region with…

2 years ago

Apple Inc. – Porter’s Five(5) Forces Analysis

The paper presents detailed overview about the Apple Inc. analysis on the parameters set by…

2 years ago

Marketing Plan – Thomson Holiday Group

The purpose of this research paper is to develop a marketing plan for the Thomson…

2 years ago

Case Study – Jerk Stars Ltd- Sales and Marketing Human Resources Dilemma

1. As applicable to other department managers, a human resources manager invigilates the departments and…

2 years ago

KFC Jamaica – Operation and Services Flow

The purpose of the present article is to formulate a work allocation flow chart of…

2 years ago