Q64. - Algebra 2

Question

PREREQUISITE SKILL Find the median of each set of numbers.

64. $\left\{\mathbf{3},\mathbf{2},\mathbf{1},\mathbf{3},\mathbf{4},\mathbf{8},\mathbf{4}\right\}$

Step-by-Step Solution

Answer

The median of the given set of numbers is 3.

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 $\frac{\left(\frac{n}{2}\right)\text{th number}+\left(\frac{n}{2}+1\right)\text{th number}}{2}$ if $n$ is even.

Step 2 – List the given data

The given set of numbers is $\left\{3,2,1,3,4,8,4\right\}$.

Step 3 – Calculate n

Counting, it is found that there are $7$ numbers in the given set. Then, $n=7$.

Step 4 – Arrange in ascending order

Arranging the given set of numbers in ascending order,

 

$\left\{1,2,3,3,4,4,8\right\}$

Step 5 – Find the median

Here, $n=7$. So, $n$ is odd.

 

Put $n=7$ in $\left(\frac{n+1}{2}\right)\text{th number}$ to get,

 

$\left(\frac{7+1}{2}\right)\text{th number}$

 

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

 

$\text{4th number}$

 

The $\text{4th number}$ in the given set after it is arranged in ascending order is 3.

 

So, the median of the given set of numbers is 3.