How to Find Median if n is Even?

To find the median of a dataset with an even number of observations (n), arrange the data in ascending order, and the median is the average of the two middle values.

This can be found by taking the value of the (n/2 + (n/2)+1)/2 term, where n is the number of observations.

Finding the median of a dataset with an even number of observations involves arranging the data in ascending order and calculating the average of the two middle values. Here’s a step-by-step explanation:

Finding the Median if n is Even

1. Arrange data in ascending order.
2. Identify the Two Middle Values:
   • For an even number of observations (n), there are two middle values.
   • The positions of the middle values are given by n/2 and (n/2)+1.
     Middle Positions = n/2 and (n/2) +1
3. Calculate the Median:
   • The median is the average of the two middle values.
     Median = (Middle value 1 + Middle value 2)/2

Example: Consider the dataset: 3,6,1,9,2,73,6,1,9,2,7 with n=6.

Sort the Data: Arranging in ascending order: 1,2,3,6,7,9.

Identify the Two Middle Positions: For n=6, the middle positions are 6/2=3 and 6/2+1=4.

Calculate the Median: The median is the average of the values at positions 3 and 4: (3+6)/2 = 4.5.

So, the median of the given dataset is 4.5.

Note:

• The median is a robust measure of central tendency that is less influenced by extreme values than the mean.
• For an even number of observations, the median is not necessarily an actual data point but rather the average of two middle values.
• This method applies to both ordered and unordered datasets, as arranging the data allows for easy identification of the middle positions.