Question

Find the median of the data: 22, 28, 34, 49, 44, 57, 18, 10, 33, 41, 66, 59.

Answer 1

Hint: First we will use formula to calculate the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data. Then we will use the formula to calculate the median by adding these middle values of the given set and then divide it by 2.

Complete step-by-step answer:
We are given that the data are 22, 28, 34, 49, 44, 57, 18, 10, 33, 41, 66, 59.
First, we will arrange the given numbers in ascending order, we get
10, 18, 22, 28, 33, 34, 41, 44, 49, 57, 59, 66
We know the formula to find the median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data.
After finding the number of observations, we have that \[n = 12\].
Substituting the value of \[n\] in the above formula, we get
\[
   \Rightarrow \dfrac{{12 + 1}}{2} \\
   \Rightarrow \dfrac{{13}}{2} \\
   \Rightarrow 6.5 \\
 \]
 So, we will take the 6th and 7th terms from the terms in ascending orders, we have 34 and 41.
We know the formula to calculate the median by adding these middle values of the given set and then divide it by 2.
Adding 34 and 41, we get
\[
   \Rightarrow 34 + 41 \\
   \Rightarrow 75 \\
 \]
Dividing the above value by 2, we get
\[
   \Rightarrow \dfrac{{75}}{2} \\
   \Rightarrow 37.5 \\
 \]
Therefore, the required value is \[37.5\].

Note: We need to know that the mean is adding the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. Do not forget any marks by adding up the values, so be prepared for that. We need to know if the value from \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data is an integer than there is only one median value or else there will be two values.