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The Median

# The Median

### 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: $4, 9, 5, 7, 6, 7$

1

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

2

We need the 3.5th value

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

3

Arrange the data in order

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

4

What is the 3.5th value?

5

Nice! 👍

The median value is $6.5$

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

1

The table shows the heights of 10 students

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

2

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.

3

Use the formula to find the median value

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

4

Which value would be the median value using the formula?

5

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.

6

Which is the modal class interval?

7

The median class interval is $1.6

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