Question

Find the average of each of the following sets.
(i) $48$, $23$, $13$, $54$, $7$
(ii) $3\text{ kg}$, $47\text{ kg}$, $92\text{ kg}$, $28\text{ kg}$

Answer 1

Hint: In this problem we need to calculate the average of the given data sets. We know that the average is the ratio of the sum of all the variables to the number of variables in the given data set. So, we need to calculate the sum of the total variables and the number of variables in the given data sets. After having those values, we can find the ratio of the both values and write it as the average of the data set.

Complete step-by-step solution:
(i)
Given data set is $48$, $23$, $13$, $54$, $7$.
The sum of the all the variables in the above given data set is given by
$\begin{align}
  & S=48+23+13+54+7 \\
 & \Rightarrow S=145 \\
\end{align}$
We can observe that the number of variables in the given data set is $n=5$.
So, the average of the given data set is given by
$\begin{align}
  & \text{Avg}=\dfrac{S}{n} \\
 & \Rightarrow \text{Avg}=\dfrac{145}{5} \\
 & \Rightarrow \text{Avg}=29 \\
\end{align}$
Hence the average of the given data set $48$, $23$, $13$, $54$, $7$is $29$.
(ii)
Given data set is $3\text{ kg}$, $47\text{ kg}$, $92\text{ kg}$, $28\text{ kg}$
The sum of the all the variables in the above given data set is given by
$\begin{align}
  & S=3+47+92+28 \\
 & \Rightarrow S=170 \\
\end{align}$
We can observe that the number of variables in the given data set is $n=4$.
So, the average of the given data set is given by
$\begin{align}
  & \text{Avg}=\dfrac{S}{n} \\
 & \Rightarrow \text{Avg}=\dfrac{170}{4} \\
 & \Rightarrow \text{Avg}=42.5 \\
\end{align}$
Hence the average of the given data set $3\text{ kg}$, $47\text{ kg}$, $92\text{ kg}$, $28\text{ kg}$is $42.5\text{ kg}$.

Note: In the second given data set we can observe that all the variables are in kilograms. So, we have added them together. If some of the variables are given in grams then we need to convert all the variables into a single unit either grams or kilograms by using the relation between the grams and kilograms and then we will proceed to calculate the average.