Q65. - Algebra 2

Question

Find the median of each set of numbers.

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

Step-by-Step Solution

Answer

The median of the given set of numbers is 6.5.

Step 1 – State the formula

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.

Step 2 – List the given data

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

Step 3 – Calculate n

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

Step 4 – Arrange in ascending order

Arranging the given set of numbers in ascending order,

 

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

Step 5 – Find the median

Here, $n=8$. So, $n$ is even.

 

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

 

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

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

 

$\frac{{\text{4}}^{\text{th}}\text{number}+5^{\text{th}}\text{ number}}{2}$

 

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

 

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

 

$\frac{6+7}{2}$ =$\frac{13}{2}$

 

            =$6.5$

 

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