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.

Median

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 = (3rd observation + 4th 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