Question

The median of the observations 30, 91, 0, 64, 42, 80, 30, 5, 117, 71 is ___________.
A.52
B.51
C.53
D.\[52.5\]

Answer 1

Hint: First we will use formula to calculate median value by first calculating \[\dfrac{{n + 1}}{2}\], where \[n\] is the number of values in a set of data and then 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 observations are 30, 91, 0, 64, 42, 80, 30, 5, 117, 71.
First, we will arrange the given numbers in ascending order, we get
0, 5, 30, 30, 42, 64, 71, 80, 91, 117
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 \[n = 10\].
Substituting the value of \[n\] in the above formula, we get
\[
   \Rightarrow \dfrac{{10 + 1}}{2} \\
   \Rightarrow \dfrac{{11}}{2} \\
   \Rightarrow 5.5 \\
 \]
 So, we will take the 5th and 6th terms from the terms in ascending orders, we have 42 and 64.
We know the formula to calculate the median by adding these middle values of the given set and then divide it by 2.
Adding 42 and 64, we get
\[
   \Rightarrow 42 + 64 \\
   \Rightarrow 106 \\
 \]
Dividing the above value by 2, we get
\[
   \Rightarrow \dfrac{{106}}{2} \\
   \Rightarrow 53 \\
 \]
Therefore, the required value is 53.

Hence, option C is correct.

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. 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.