A variate X takes values 2, 9, 3, 7, 5, 4, 3, 2, 10. What is the median?

Concept:

Median: The median is the middle number in a sorted, ascending or descending, list of numbers.

Case 1: If the number of observation (n) is even

\({\rm{Median\;}} = {\rm{\;}}\frac{{{\rm{value\;of\;}}{{\left( {\frac{{\rm{n}}}{2}} \right)}^{{\rm{th}}}}{\rm{\;observation\;}} + {\rm{\;\;value\;of\;}}{{\left( {\frac{{\rm{n}}}{2}{\rm{\;}} + 1} \right)}^{{\rm{th}}}}{\rm{\;observation}}}}{2}\)

Case 2: If the number of observation (n) is odd

\({\rm{Median\;}} = {\rm{value\;of\;}}{\left( {\frac{{{\rm{n}} + 1}}{2}} \right)^{{\rm{th}}}}{\rm{\;observation}}\)

Calculation:

Given values 2, 9, 3, 7, 5, 4, 3, 2, 10

Arrange the observations in the ascending order:

2, 2, 3, 3, 4, 5, 7, 9, 10

Here, n = 9 = odd

As we know, If n is odd then,

\({\rm{Median\;}} = {\rm{value\;of\;}}{\left( {\frac{{{\rm{n}} + 1}}{2}} \right)^{{\rm{th}}}}{\rm{\;observation}} = 5^{\rm{th}}{\rm{\;observation}}\)

Hence Median = 4