To solve different types of problems on average we need to follow the properties of arithmetic mean.
Here we will learn about all the properties and proof the arithmetic mean showing the step-by-step explanation.
What are the properties of arithmetic mean?
The properties are explained below with suitable illustration.
Property 1:
If x is the arithmetic mean of n observations x_{1}, x_{2}, x_{3}, . . x_{n}; thenNow we will proof the Property 1:
We know that
Property 2:
The mean of n observations x_{1}, x_{2}, . . ., x_{n} is x. If each observation is increased by p, the mean of the new observations is (x + p).Now we will proof the Property 2:
x = (x_{1} + x_{2} +. . . + x_{n})/nProperty 3:
The mean of n observations x_{1}, x_{2}, . . ., x_{n} is x. If each observation is decreased by p, the mean of the new observations is (x - p).Now we will proof the Property 3:
x = (x_{1} + x_{2} +. . . + x_{n})/nProperty 4:
The mean of n observations x_{1}, x_{2}, . . .,x_{n} is x. If each observation is multiplied by a nonzero number p, the mean of the new observations is px.Now we will proof the Property 4:
x = (x_{1} + x_{2} + . . . + x_{n})/nProperty 5:
The mean of n observations x_{1}, x_{2}, . . ., x_{n} is x. If each observation is divided by a nonzero number p, the mean of the new observations is (x/p).Now we will proof the Property 5:
x = (x_{1} + x_{2} + ... + x_{n})/nTo get more ideas students can follow the below links to understand how to solve various types of problems using the properties of arithmetic mean.
Statistics
Word Problems on Arithmetic Mean
Properties Questions on Arithmetic Mean
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