Question

The median of the following series $520,20,340,190,35,800,1210,50,80$is:
A. $1210$
B. $520$
C. $190$
D. $35$

Answer 1

Hint: According to the question given in the question we have to determine the median of the following series $520,20,340,190,35,800,1210,50,80$. So, first of all we have to rearrange all the given numbers in ascending order means we have to arrange all the numbers from minimum number to maximum number.
Now, we have to find the total number of observations with the help of the given series and then we have to find the median for the given series which can be determined with the help of the formula to find the median which is as explained below:
$ \Rightarrow $Median$ = {\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$observation $.........................(A)$
So, if the number of given observations are odd then we have to apply the formula (A) to determine the median. Then after determining the observation number we have to check for the median.

Complete step-by-step solution:
Step 1: First of all we have to rearrange all the given number in ascending order means we have to arrange all the numbers from minimum number to maximum number which is as below:
$ \Rightarrow 20,35,50,80,190,340,520,800,1210$
Step 2: Now, we have to count the total number of observations to determine that the given numbers are even in count or odd in count. Hence,
$ \Rightarrow n = 9$ which is odd.
Step 3: As from step 2 we have determined that the total number of observations are odd so, we have to use the formula (A) as mentioned in the solution hint.
$ \Rightarrow $Median
$ = {\left( {\dfrac{{9 + 1}}{2}} \right)^{th}}$
$ = {\left( {\dfrac{{10}}{2}} \right)^{th}}$
$ = {5^{th}}$ observation.
Step 4: Now, we have to determine the observation number from the obtained ascending number of series we have to check for the median. Hence,
$ \Rightarrow {5^{th}}$ observation is $ = 190$
Final solution: Hence, with the help of the formula (A) as mentioned in the solution hint we have determined the median which is 190.

Therefore option (C) is correct.

Note: To determine the median for the given data it is necessary that we have to find the total number of given observation and of the total number of given observation is odd then to find the median we have to use the formula ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$
If the total number of observations are even then there will be two median which can be obtain by finding the observations which are ${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$ and ${\left( {\dfrac{n}{2} + 1} \right)^{th}}$ observations.