Question

What is the average of the first five multiples of \[12\]?
(A) \[36\]
(b) \[38\]
(c) \[40\]

Answer 1

Hint: In this question we are going to find the average of first five multiples of \[12\] .The formula for finding the average, \[ Average = \dfrac{{Sum\; of \;numbers}}{{total \;numbers}}\] and then calculate the sum of the first five multiples and divide the sum by \[5\] to get the average. Finally, we get the required solution.

Complete step-by-step answer:
A multiple is the product that we get when one number is multiplied by another number.
In order to determine the first five multiples of \[12\], Let’s multiply \[12\] by \[1\] to \[5\],that is, the multiplication table of \[12\].
\[12 \times 1 = 12\]
\[12 \times 2 = 2\]
\[12 \times 3 = 36\]
\[12 \times 4 = 48\]
\[12 \times 5 = 60\]
To find the average we add up all the values and then divide this total by the number of values. Here the number of values is \[5\], so divide the sum \[ Average = \dfrac{{Sum\; of \;numbers}}{{total \;numbers}}\]

\[ = \dfrac{{12 + 24 + 36 + 48 + 60}}{5}\]
On further simplification, then
\[ = \dfrac{{170}}{5}\]
\[ Average = 36\].
Therefore, the average of the first five multiples of \[12\] is \[36\].
Hence, option (A) \[36\] is correct.
So, the correct answer is “Option A”.

Note: The average value in a set of numbers is the middle value. In the above set of values \[36\] is the middle value and it’s the average too.
Example: Find the average of \[24{{,}}55{{,}}17{{,}}87{{,}}100\].
To find the average of the above numbers by finding the middle value first write the numbers in either ascending or descending order.
Here we use ascending order and the numbers are \[{{17,24,55,}}87{{,}}100\]. The total number in the set is \[5\], which is an odd number. Since we cannot find the absolute average just by finding the middle value. In such case we only get approximate value hence in such situations we must use the method,
\[ Average = \dfrac{{Sum\; of \;numbers}}{{total \;numbers}}\]
In the above example the middle value is \[55\], therefore the approximate average is \[55\] and the absolute value will be around \[55\] and can be in decimal also.
\[ = \dfrac{{17 + 24 + 55 + 87 + 100}}{5}\]
\[ = \dfrac{{283}}{5}\]
\[ Average = 56.6\]
Hence, use the middle value method only if the numbers in the set are even, otherwise use the average formula to find the average.