Question

What is the median for the following observations: \[2,5,8,4,9,6,7\]
A. \[6\]
B. \[8\]
C. \[4\]
D. \[4.5\]

Answer 1

Hint: The median is the middle value of the given observations when arranging the observations in an ascending or descending order. It is known as a measure of central tendency. So, to find the median of given observations, atfirst arrange those observations in ascending or descending order and then use the formula of median. The formula is different for even and odd numbers of observations.

Formula Used:
If the total number of observations is odd, then the formula of the median is
Median = \[\left( {\dfrac{{n + 1}}{2}} \right)\]-th observation, where \[n\] is the number of given observations.
If the total number of observations is even, then the formula of the median is
Median = The average of \[\left( {\dfrac{n}{2}} \right)\]-th observation and \[\left( {\dfrac{n}{2}} \right) + 1\]-th observation, where \[n\] is the number of given observations.

Complete step by step solution:
The given observations are \[2,5,8,4,9,6,7\].
Arrange the observations in ascending or descending order.
Let us take ascending order.
After arranging in ascending order, we get \[2,4,5,6,7,8,9\]
Count the number of observations.
The number of observations is \[7\].
So, \[n = 7\], which is odd.
Use the formula to calculate the median for odd number observations.
So, median = \[\left( {\dfrac{{7 + 1}}{2}} \right)\]-th observation i.e. the \[4\]-th observation.
Find the \[4\]-th observation from the given observations.
The \[4\]-th observation is \[6\].
So, the median of the given observations is \[6\].

Option ‘A’ is correct

Note: Here we have used the formula to calculate the odd number of the Median = \[\left( {\dfrac{{n + 1}}{2}} \right)\]. Do not mess up with the formula to calculate the median for odd or even number observations. Also, without arranging the terms properly, one will not get the median.