Properties of Arithmetic Mean

Introduction of arithmetic mean properties:

In math and statistics, the arithmetic mean or mean defines group of values is sum of all the values in the group and divide it by the number of items in the group. Based on list or group the name of mean is varied that is if the list defines the statistical population then the mean of the population is known as the population mean. Likewise if the group defines the statistical sample then it is known as sample mean.

Properties of Arithmetic Mean:

Let we see about some of the properties of arithmetic mean.

Arithmetic mean Property 1:

If m1 and m2 are the means of the two lists defined from the values v1 and v2 then the mean m is given by the equation
m = v1m1+v2m2/ v1+v2

Arithmetic mean Property 2:

If each inspection in the data is converted by m, the sum total of all the values unaffected.
That is, m = m1, m2, m3, m4........, mn / v
thus m1,m2,m3,m4........,mn = vm
Replacing each observation by m, we obtains

m+m+m........+m = vm

Arithmetic mean Property 3:

If all value of the variable m is either improved, reduces, divided or multiplied by a constant, the explanation so acquired also improved, reduces, acquire multiplied or acquire divided correspondingly by the similar constant.Please express your views of this topic Solve Equation by commenting on blog.

Arithmetic mean Property 4:

Algebraic sum of the divergence of a group of values from their arithmetic mean is 0.

Example:

Example 1:

Find the mean of the given values 56,35,87,23,63,58,46.

Solution:

We know the formula for find the mean, that is, addition of all the values/ total number of values.

Therefore, 56+35+87+23+63+58+46/7

= 368/7

= 52.571

Example 2:

Find the sum of the deviations of the given different values 5, 10, 15, 20, 25 from their mean.

Solution
Mean of 5, 10, 15, 20, 25 is,

`barx=(5+10+15+20+25)/(5)=(75)/(5)=15`



Therefore the addition of the deviation about mean is 0.