# Estimating by Clustering

The word in itself means grouping, a bunch or to gather. In all this type of estimation is mostly used when estimating the products of a group of numbers. Therefore clustering procedure can be applied if and only if all the numbers are close to a certain number.

Example

Estimating by Clustering:  98 + 99 + 103 + 101+ 105 + 103

Solution

As we can see all the numbers are clustering around 100. In all there are 6 numbers. The sum is about 6 x 100 = 600

Let say we want to verify how far we are from the actual result. We just add the numbers from the original problem and compare it to the numbers that have been estimated.

We have 98 + 99 + 103 + 101 + 105 + 103 = 609

Sure enough 600 is close to 609.

As for adding, the same principal is applied again.

Example

Estimating by clustering: 754 + 753 + 751 + 748+ 746

Solution

Again we see that all the numbers are clustered around 750, and there are a total of 5 numbers.

Therefore 5 x 750 = 3750.

In the case that you are not sure where the number 5 came from, just add 750 +750 + 750+ 750 + 750 = 3750. So the 5 come from on how many 750 are there.

In our case there are 5

Just the sake argument let us verify our results to see if we are near the real answer. In fact, the original problem is:

754 + 753 + 751 + 748 + 746 = 3752.

Thus 3750 is in reality close to the answer.