Question

What is the average (arithmetic mean) of the $3$ quantities in the list below?
 $12 - n,12,12 + n$
(A) $4$
(B) $12$
(C) $18$
(D) $4 + \dfrac{n}{3}$
(E) $12 + \dfrac{n}{3}$

Answer 1

Hint: Arithmetic mean represents a number that is obtained by dividing the sum of the elements of a set by the number of values in the set. Now first we will list the given $3$ quantities . After making a list we find the sum of these numbers. Now we know the total number of values is $3$ . The formula to calculate Arithmetic mean is $\dfrac{{{\text{sum of all the values}}}}{{{\text{Number of total values}}}}$ . Hence using formula we can find the Arithmetic mean of the given quantities.

Complete step-by-step solution:
Now first let us list the given $3$ quantities.
Hence the given quantities are $12 - n,12,12 + n$ .
Now we want to find the Arithmetic mean of the given quantities
Arithmetic mean value is nothing but the average of given data.
Now the sum of all these quantities
$12 - n + 12 + 12 + n$
Omit the similar term and get
$ = 12 + 12 + 12$
$ = 36$
Now the total quantity in the given data is $3$ .
Hence the Arithmetic mean of the given data is $\dfrac{{36}}{3}$
$ = 12$
Therefore the Arithmetic mean of $12 - n,12,12 + n$ is $12$ .
Option (B) is correct.

Note: For small quantities problems, we can use the above method and we get the result. For the harder problem and n-th term problem we use a formula to find the Arithmetic mean. Suppose we have to find the arithmetic mean of the first $10$ natural number. Then we use the formula $\dfrac{{{\text{first number + last number}}}}{2}$ i.e., $\dfrac{{1 + 10}}{2} = \dfrac{{11}}{2} = 5.5$ . Hence we can use this for quick calculation. Just remember this can be used only if terms are in Arithmetic Progression.