Question

Find the mean of the first five multiples of $7$.
$\begin{align}
  & (a)18 \\
 & (b)21 \\
 & (c)15 \\
 & (d)24 \\
\end{align}$

Answer 1

Hint: In this question, we have to find the meaning of the data. Here we are not given as such numbers, but we are given data as the first five multiples of 7.Since mean is average, where we add up all the numbers and then divide it by the number of numbers, so we need the numbers. Hence, we will first find the first five multiples of 7, after that we will add them to get the sum of the terms and then divide it by the number of terms which is five.

Complete step-by-step answer:
Here we have to find the first five multiples of $7$, which will be obtained by multiplying $7$ by the first five natural numbers.
\[\begin{align}
  & 7\times 1=7 \\
 & 7\times 2=14 \\
 & 7\times 3=21 \\
 & 7\times 4=28 \\
 & 7\times 5=35 \\
\end{align}\]
Hence, we have obtained data as $7,14,21,28,35$.
Here, we can see that the number of terms $=35$
Let us now find the sum of the terms which is $7+14+21+28+35=105$.
Sum of terms $=105$.
As we know, $Mean=\dfrac{Sum~of~terms}{No.~of~terms}$
Therefore, $Mean=\dfrac{105}{5}=21$

Hence, the mean of the first five multiples of $7$ is $21$.

So, the correct answer is “Option (b)”.

Note: Always note that the mean may or may not be a value from the original list. It is a common result. Students should not assume that the mean will be one of the original numbers. While calculating five multiples of $7$, make sure you count multiples from one only. Don’t take zero as one of the multiple. Students can always use empirical formulas for calculating mean, median or mode, but it is more difficult than the direct method. Mean is just the average of the data, so we simply divide the sum of data by the number of terms of data to obtain the required answer.