Median Calculator

How to Calculate the Median

The median is a measure of central tendency that represents the middle value in a sorted dataset. It's particularly useful when dealing with skewed distributions or datasets with extreme values.

Median Formula

To calculate the median:

1. Sort the dataset in ascending order.
2. If the number of values (n) is odd:

   \[ \text{Median} = x_{\frac{n+1}{2}} \]

   Where \(x_{\frac{n+1}{2}}\) is the middle value.
3. If the number of values (n) is even:

   \[ \text{Median} = \frac{x_{\frac{n}{2}} + x_{\frac{n}{2}+1}}{2} \]

   Where \(x_{\frac{n}{2}}\) and \(x_{\frac{n}{2}+1}\) are the two middle values.

Calculation Steps

1. Sort the dataset in ascending order.
2. Determine if the number of values is odd or even.
3. If odd, select the middle value.
4. If even, calculate the average of the two middle values.

Example

Let's calculate the median for the dataset: 4, 7, 9, 3, 2, 7

1. Sort the dataset: 2, 3, 4, 7, 7, 9
2. Count the values: n = 6 (even)
3. Find the two middle values: 4 and 7
4. Calculate the average of the middle values:

   \[ \text{Median} = \frac{4 + 7}{2} = \frac{11}{2} = 5.5 \]

Visual Representation

This diagram illustrates the median for the example dataset. The red dashed line represents the median value (5.5), which lies between the two middle values (4 and 7) when the dataset is sorted.