Question

Find the average and median of 4.2, 7.4 and 8.8

Answer 1

Hint: We solve this problem by using the simple formula of average.
We have the formula of an average of ungrouped data as \[\Rightarrow Avg=\dfrac{\text{Sum of observations}}{\text{number of observations}}\]
By using the above formula we find the average of given numbers.
Then we find the median which is given as the middle value of given numbers after arranging them in ascending order. If the number of observations is even then the average of idle two terms gives the median of the data.

Complete step by step answer:
We are given that the numbers as
4.2, 7.4, 8.8
Here, we can see that there are 3 numbers given.
Let us assume that the number of numbers as \[\Rightarrow n=3\]
Now let us assume that the sum of given observations as \[S\]
Now, by adding the given numbers we get the sum of observations as
\[\begin{align}
  & \Rightarrow S=4.2+7.4+8.8 \\
 & \Rightarrow S=20.4 \\
\end{align}\]
Now, let us assume that the average of given three numbers as \[A\]
We know that the formula of average of a ungrouped data as
\[\Rightarrow Avg=\dfrac{\text{Sum of observations}}{\text{number of observations}}\]

By using the above formula we get the average of given numbers as
\[\Rightarrow A=\dfrac{S}{n}\]
Now, by substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow A=\dfrac{20.4}{3} \\
 & \Rightarrow A=6.8 \\
\end{align}\]
Therefore, we can conclude that the average of given three numbers is 6.8
Now, let us calculate the median of the given data.
We know that the median of data is given as the middle value of given numbers after arranging then in ascending order
Now, let us arrange the given numbers in ascending order then we get
4.2, 7.4, 8.8
Here, we can see that the middle value is 7.4.
Therefore we can conclude that the median of the given data is 7.4

Note:
Students may get confused between the mean and average
The mean and average both are the same in ungrouped data.
The formula of an average of ungrouped data as
\[\Rightarrow Avg=\dfrac{\text{Sum of observations}}{\text{number of observations}}\]
Also, the formula of the mean of ungrouped data as
\[\Rightarrow mean=\dfrac{\text{Sum of observations}}{\text{number of observations}}\]
Here, we can see that both are the same.
Also, students may do mistakes in finding the median of the data.
First, we need to arrange the given observations in ascending or descending order to get the median.
But students may take the middle value of the given data in the given order which will be the wrong answer.