Question

What is the median of the observations 36, 48, 29, 62, 71 and 84?

Answer 1

Hint: We first explain the concept of median and the differences for discrete data and continuous data. The even number of discrete inputs make the median similar to the average of the middle numbers of the ordered sequence.

Complete step by step answer:
It is mentioned here that we are finding the median of the observations 36, 48, 29, 62, 71 and 84.
Individual numbers mean we are dealing with discrete data.
In case of discrete data, the Median is the number in an ordered series midway between the range extremes.
We arrange the values in either increasing or decreasing order and then find the middle value of them.
When there are an odd number of values, we can just find the value so that there are the same number of values above as there are below this middle value. When there is an even number of values, there is an issue if there is not one number that acts as a middle value. Instead, the two middle numbers such that there are the same number of values above as below these two middle numbers. As a compromise, we take the average of these two middle numbers.
For the observations 36, 48, 29, 62, 71 and 84, we get the ordering as $29,36,48,62,71,84$.
The middle numbers are 48 and 62. So, median becomes $\dfrac{48+62}{2}=\dfrac{110}{2}=55$.

Note: Usually the average is very different from the mean or average. The median is more shifted towards the middle of the number of values irrespective of the difference between numbers and their individual values.