# Find the median of a set of even numbers

## Question: How to find the median of a set of even numbers?

The median represents the middle value for any group. It is the point at which half the data is more and half the data is less.

## Answer: For an even set of numbers Median = ( (n/2)^{th }observation+(n/2 +1)^{th }observation ) / 2

The value of the middle-most observation obtained after arranging the data in ascending order is called the medianof the data.

## Explanation:

Note that the median is the value at the mid-point of the dataset, not the mid-point of the values.

Let us look at an example:

Annie noted the number of cakes she baked every day over the past week. If the numbers were: 1, 2, 2, 3, 4, 3. What is the median value of the cakes she baked?

Step 1: Arrange the data items in ascending order.

Original set: {1,2,2,3,4,3}, Ordered Set: {1,2,2,3,3,4}

Step 2: Count the number of observations.

Number of observations n = 6(even)

Step 3: ( (6/2)^{th }observation+(6/2 +1)^{th }observation ) / 2

Median = (3^{rd} observation + 4^{th} observation)/ 2 = (2+3)/2 = 2.5

So the median value of the cakes Annie baked is 2.5

### Hence, for an even set of numbers Median = ( (n/2)^{th }observation+(n/2 +1)^{th }observation ) / 2

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