Question

Find the arithmetic mean of numbers 2 and 8.
(A) 5
(B) 10
(C) 16
(D) 3.2

Answer 1

Hint: The formula to determine the arithmetic mean between two numbers $a$ and $b$ is given as $\dfrac{{a + b}}{2}$. Use this formula and put the given numbers to find the arithmetic mean.

Complete step-by-step answer:
According to the question, we have to determine the arithmetic mean of two numbers 2 and 8.
We know that the formula to determine the arithmetic mean between two numbers $a$ and $b$ is given as:
$ \Rightarrow A.M. = \dfrac{{a + b}}{2}$
If we put $a = 2$ and $b = 8$ in the above formula, we’ll get:
$ \Rightarrow A.M. = \dfrac{{2 + 8}}{2}$
Simplifying it further, we’ll get:
$
   \Rightarrow A.M. = \dfrac{{10}}{2} \\
   \Rightarrow A.M. = 5 \\
 $
Thus the arithmetic mean of two numbers 2 and 8 is 5. Hence (A) is the correct option.
Additional Information:
The formula to determine the arithmetic mean between $n$ numbers ${a_1},{\text{ }}{a_2},.....,{\text{ }}{a_n}$ is given as:
$ \Rightarrow A.M. = \dfrac{{{a_1} + {a_2} + .... + {a_n}}}{n}$
For two numbers $a$ and $b$, this will become:
$ \Rightarrow A.M. = \dfrac{{a + b}}{2}$
Similarly, the formula to determine geometric mean between these numbers is:
$ \Rightarrow G.M. = {\left( {{a_1}.{a_2}.{a_3}....{a_n}} \right)^{\dfrac{1}{n}}}$
For two numbers $a$ and $b$, this will become:
$ \Rightarrow G.M. = \sqrt {ab} $

And the formula to determine the harmonic mean between the same numbers is:
$ \Rightarrow H.M. = \dfrac{n}{{\dfrac{1}{{{a_1}}} + \dfrac{1}{{{a_2}}} + ..... + \dfrac{1}{{{a_n}}}}}$
For two numbers $a$ and $b$, this will become:

$ \Rightarrow H.M. = \dfrac{{2ab}}{{a + b}}$

Note:
The arithmetic mean between $n$ numbers is also the average value of $n$ observations with the value of each observation is the same as the value of corresponding number. Thus the formula for the average of $n$ observations, ${a_1},{\text{ }}{a_2},.....,{\text{ }}{a_n}$, is also same and it is:
$ \Rightarrow {\text{Average}} = \dfrac{{{a_1} + {a_2} + .... + {a_n}}}{n}$
Further, the arithmetic mean between two integers is always the number lying exactly between these two integers on the number line. It can be both integer and decimal.