Question

PREREQUISITE SKILL Find the median of each set of numbers.

66. $\left\{\mathbf{138},\mathbf{235},\mathbf{976},\mathbf{230},\mathbf{412},\mathbf{466}\right\}$

Short answer

The median of the given set of numbers is 323.5.

Step-by-step solution

– 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.

– List the given data

The given set of numbers is $\left\{138,235,976,230,412,466\right\}$.

– Calculate n

Counting, it is found that there are $6$ numbers in the given set. Then, $n=6$.

– Arrange in ascending order

Arranging the given set of numbers in ascending order,

$\left\{138,230,235,412,466,976\right\}$

– Find the median

Here, $n=6$. So, $n$is even.

Put $n=6$in $\frac{\left(\frac{n}{2}\right)\text{th number}+\left(\frac{n}{2}+1\right)\text{th number}}{2}$to get,

$\frac{\left(\frac{6}{2}\right)\text{th number}+\left(\frac{6}{2}+1\right)\text{th number}}{2}$

$\frac{\left(3\right)\text{th number}+\left(3+1\right)\text{th number}}{2}$

$\frac{\text{3rd number}+4\text{th number}}{2}$

The $\text{3rd number}$and the $\text{4th number}$in the given set after it is arranged in ascending order are 235 and 412 respectively.

Put $\text{3rd number}=235$and $\text{4th number}=412$in $\frac{\text{3rd number}+4\text{th number}}{2}$to get,

$\frac{235+412}{2}$

$\frac{647}{2}$

$323.5$

So, the median of the given set of numbers is 323.5.