Math for Nurses chapter trying

hfriedman

33 Math for Nurses chapter trying

https://pressbooks.bccampus.ca/numeracy/chapter/descriptive-statistics/

Median

The median is the middle point in a data set, once the values have been listed in numerical order. If there are an odd number of values in the data set, the value of the median is exactly the same as the number in the physical middle of the data set. If there are an even number of values, the middle is considered to be the value that would fall between the two numbers in the middle. The examples following illustrate the difference in physical location of the median in data sets with odd and even numbers of values.

Odd Number of Values
$\begin{array}{ccccc} &&\text{median}&& \\ &&\downarrow&& \\ 2&6&8&10&15\end{array}$

Even Number of Values
$\begin{array}{ccccc} &&\text{median}&& \\ &&\downarrow&& \\ 2&6&\text{ }&8&15 \\ &&=7&&\end{array}$

It is easy to identify where the middle is in the examples above because the middle point is visually easy to identify. In larger data sets, a formula can be used to identify the location of the middle.

$\dfrac{n+1}{2}=\text{location of median}$

For a data set with an odd number of values the formula gives the location of where the value would be in a numbered list of values. In the example above, the median is the third number in the list and so the formula for finding the median in this set gives the number 3. You can see that the location, 3, and the median, 8, are different numbers. This can be confusing for some people. The formula just gives the location, or place of the number, in the list of values. Once the formula gives the location, you need to figure out which value is at that particular place in the list. The process for using the formula is summarized in the box below.

Using align:

$\text{location of median}$ [latex]\begin{align*}&=\dfrac{n+1}{2} \\ \\
&=\dfrac{5+1}{2} \\ \\
&=3\end{align*}[/latex]