Question

What is the median of a data set?

Answer 1

Hint: The median is the middle most number in the given sequence of the numbers when arranged by the rank either in ascending or the descending order. It is denoted by “M”. When the given numbers are odd, median $ M = \dfrac{{n + 1}}{2} $ and when their given numbers are even, do sum of two middle terms and divide them by two.

Complete step-by-step answer:
Let us take one example: Find the median of: $ 66,98,54,92,87,63,72 $
Here, given numbers of numbers in the sequence are $ 7 $
 $ \therefore n = 7 = odd $
Now, median $ M = \dfrac{{n + 1}}{2} $
Place the value of “n” in the above equation –
 $
  M = \dfrac{{7 + 1}}{2} \\
   \Rightarrow M = \dfrac{8}{2} \\
   \Rightarrow M = 4 \;
  $
Given sequence: $ 66,98,54,92,87,63,72 $
Now, arrange the given sequence in ascending order and the fourth term in the sequence will be the Median.
Ascending order: $ 54,63,66,72,87,92,98 $
From the above sequence, fourth term is $ 72 $
Hence, the median M is $ 72 $

Note: Remember the difference between mean and median. Mean is the sum of all the numbers upon the total number of the numbers. Mean is affected by the extreme values of the sequences while in the median extreme values do not affect the extreme values. The above sequence can be solved by arranging in the descending order.