Question

Find the median of the given observation $15,20,45,30,60,36$.
(A) $32$
(B) $33$
(C) $47.5$
(D) None of the above

Answer 1

In this question, the given observations are $15,20,45,30,60,36$.
We have to find the median of the given observations.
We know that the median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
We need to first arrange the given observations in ascending or descending order then we need to find the number of the observations if there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above or if there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value. Then we can easily find out the required solution.

Complete step-by-step solution:
The given observations are $15,20,45,30,60,36$.
We need to find out the median of the given observations.
Median is the middle most value of a series. So when the series has an odd number of elements then the median can be calculated easily but when the series has an even number of elements then the series has two middle values, so the median is calculated by taking out the average of both the values.
We need to first arrange the given observations into ascending order.
Thus we get, the observations as $15,20,30,36,45,60$
The formula to calculate the median is ${\left( {\dfrac{{N + 1}}{2}} \right)^{th}}$ term of the series where N is the number of observations.
The number of observations in the series is $6$ which is even, so the series has two middle values, $30,36$ (${3^{rd}}\& {4^{th}}$ term) and median is calculated by taking out the average of both the value.
Then the median =$\dfrac{{30 + 36}}{2} = \dfrac{{66}}{2} = 33$ .
Hence the median of the given observations $15,20,45,30,60,36$ is $33$ .

$\therefore$ The option (B) is the correct option.

Note: In statistics and probability theory, a median is a value separating the higher half from the lower half of a data sample, a population or a probability distribution. For a data set, it may be thought of as "the middle" value.
If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.