Question

Find the median of:
3, 11, 7, 2, 5, 9, 9, 2, 10

Answer 1

Hint: The question is related to the statistics topic. Here we have to determine the median for the given observations. The observation is in the form of ungrouped data and median for the ungrouped data is the middle term of the observation then by finding the $${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$$ term of given observation, we can determine the required median.

Complete step by step answer:
The observation is in the form of ungrouped data where we do not know the value of frequency. In the ungrouped data first we arrange the observations in the ascending order.
Now consider the given observations.
3, 11, 7, 2, 5, 9, 9, 2, 10.
On arranging the above observations in the ascending order, we have
2, 2, 3, 5, 7, 9, 9, 10, 11.
The number of observations are 9 i.e., $$n = 9$$.
To determine the median for the ungrouped data we have two formulas. If the number of observations is in odd number the formula is $${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$$ observation if it is in even number we have two observations then the formula is $${\left( {\dfrac{n}{2}\,} \right)^{th}}$$observation and $${\left( {\dfrac{n}{2} + 1} \right)^{th}}$$ observations
The number 9 is the odd number, the median of the given observation is the value of $${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$$term.
On substituting the value of n we have
$$ \Rightarrow \,\,\,{\left( {\dfrac{{9 + 1}}{2}} \right)^{th}}$$ term.
$$ \Rightarrow \,\,\,{\left( {\dfrac{{10}}{2}} \right)^{th}}$$ term
On simplification, we get
$$ \Rightarrow \,\,\,{5^{th}}$$ term
Hence, the value of the $${5^{th}}$$ term is $$7$$.
Therefore, the median of the given observation is $$7$$.

Note:
 Remember, when finding the median of ungrouped data, first arranging the given data in an ascending or descending order of magnitude the value of the middle most observation is known as the median of data.
‘$$n$$’ is a number of observations:
If $$n$$ is odd, then
$$\therefore $$ median = value of $${\left( {\dfrac{{n + 1}}{2}} \right)^{th}}$$term.
If $$n$$ is even, then
$$\therefore $$ median = value of $${\left( {\dfrac{n}{2}} \right)^{th}}$$ and $${\left( {\dfrac{n}{2} + 1} \right)^{th}}$$ term.