Probability & Statistics

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The Median

Another way of analysing the average of a set of data is by finding the median, which is the middle value when the data is arranged in order.

Another way of analyzing and describing the average of a set of data is by looking at the median value, which is the middle value within a set of data. The median can be more easily identified when a set of data is presented in order.

The position of the middle value of a data set can be identified using the following formula.

$\dfrac{n + 1}{2}$

Where $n$ is the total number of values.

Let's start with a set of values: $1.67 m, 1.58 m, 1.62 m, 1.73 m, 1.75 m$

We can use the formula here to find the middle value. There are five total values in the set, so the formula becomes:

$\dfrac{5 + 1}{2} = 3$

The middle value is therefore the 3rd value. We can see this when the values are in order:

$1.67 m, \space 1.58 m,\space {\color{#21affb}1.62 m}, \space1.73 m, \space1.75 m$

Here is a set of data collected on the shoe sizes of 10 students: $4, 9, 5, 7, 6, 7$

Solve the formula $\dfrac{n+1}{2}$

We need the 3.5th value

We can find this adding together the 3rd and 4th values, and dividing this number by 2.

Arrange the data in order

$4,5,{\color{#21affb}6,7},7,9$

What is the 3.5th value?

Nice! 👍

The median value is $6.5$

Here is a list of numbers, what is the median? $1, 2, 3, 5, 8, 9, 9$

The table shows the heights of 10 students

We can not identify exactly what the median height as the data is grouped.

However, we can identify the median class interval

To find this, we need to keep a running total. In doing this, we can easily see which interval the median value is located in.

Use the formula to find the median value

$\dfrac{n+1}{2}$

Which value would be the median value using the formula?

Find the 5.5th value in the running total

By looking at the running total, we can easily spot which interval the 5.5th value is located in.

Which is the modal class interval?

The median class interval is $1.6<x\le 1.7$

Nice! Even though we do not have a specific value, we have a good range in which the median would lie.