Find the median of each set of numbers.

$\left\{\mathbf{9},\mathbf{3},\mathbf{7},\mathbf{5},\mathbf{6},\mathbf{3},\mathbf{7},\mathbf{9}\right\}$

The median of a set of $n$numbers arranged in ascending order, is ${\left(\frac{n+1}{2}\right)}^{\text{th}}$number in the set if $n$is odd and $\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{number}+{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{number}}{2}$if $n$is even.

The given set of numbers is $\left\{9,3,7,5,6,3,7,9\right\}$.

Counting, it is found that there are $8$ numbers in the given set. Then, $n=8$.

Arranging the given set of numbers in ascending order,

$\left\{3,3,5,6,7,7,9,9\right\}$

Here, $n=8$. So, $n$is even.

Put $n=8$in localid="1647257515762" $\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{number}+{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{number}}{2}$to get,

localid="1647257593332" $\frac{{\left(\frac{8}{2}\right)}^{\text{th}}\text{number}+{\left(\frac{8}{2}+1\right)}^{\text{th}}\text{number}}{2}$

localid="1647257598946" $\frac{{\left(4\right)}^{\text{th}}\text{number}+{\left(4+1\right)}^{\text{th}}\text{number}}{2}$

localid="1647257609702" $\frac{{\text{4}}^{\text{th}}\text{number}+5^{\text{th}}\text{number}}{2}$

The localid="1647257619915" ${\text{4}}^{\text{th}}\text{number}$and the localid="1647257628530" $5^{\text{th}}\text{number}$in the given set after it is arranged in ascending order are 6 and 7 respectively.

Put localid="1647257637218" ${\text{4}}^{\text{th}}\text{number}=6$and localid="1647257649419" ${\text{5}}^{\text{th}}\text{number}=7$in localid="1647257662514" $\frac{{\text{4}}^{\text{th}}\text{number}+5^{\text{th}}\text{number}}{2}$to get,

$\frac{6+7}{2}$=$\frac{13}{2}$

=$6.5$

So, the median of the given set of numbers is 6.5.