Weighted Average

Average is necessary to generalise a set of data. Average is a value that could represent an entire data set. Because of average, instead of going to the trouble of reading the whole data set, you can refer to the value of average. Average is pretty useful for manufacturing and marketing industries to determine the target audience.

In simple average, we consider all values of equal importance and calculate the average accordingly. However, there is another type of average called the weighted average. In weighted average different quantities are assigned different degrees of importance, and accordingly average is calculated.

Weighted Average

The weighted average can be a fairly new concept to most students. We have all dealt with the normal type of average and problems based on it. However, while preparing for CLAT, it’s important to know the concept of weighted average, the weighted average formulas, and the weighted average method to solve a few questions from the quantitative section.

Let’s understand what exactly is a weighted average.

The weighted average is the average where each quantity in the data set is assigned with a weight. The weight is predetermined.

The weighted average is considered more accurate than the normal average because, in the real world, some quantities are more important than others.

Use of Weighted Average

Following are the uses of the weighted average concept:

• The concept of weighted average could be used to equalise the frequency of quantities in a particular data set.
• For example, there is a survey which is collecting information from various age groups. However, they couldn’t get many opinions from the 10-18 age group. So, in order to represent views of all age groups in equal proportions, the age group 10-18 will be assigned more weight.
• Another way the weighted averages could be used is if a particular aspect is more important than the other.
• Suppose there is a test for engineering students on the topic’s physics, chemistry, and mathematics. The examiners may view mathematics as a more important subject than the other two, and hence more weight would be assigned to mathematics in average marks.

The Weighted Average Method

The method to calculate the weighted average differs from the simple average method.

The set of numbers must be multiplied by their weights before adding all the numbers up to get the final average.

The following steps are involved in the calculation of the weighted average.

Note that this method is for averages with weights in decimal points. 

Identifying the weight of each data entity:

It would help if you determined first which quantities are more important than the others. 

In data mining applications, randomised trees are used for this purpose. 

However, in examinations like the CLAT, they will provide you with a column of weights right next to the data entities. 

Multiplying each data quantity by its weight:

Once you have determined the weight of each data entity, you have to multiply the weights with their respective quantities. 

Addition of the quantities

Now you have to add all the multiplication products from the above step, and you will have your weighted average. 

However, when the weights of data entities aren’t given in a fraction, the way to calculate the average differs. 

The weighted average method for when weights don’t add up to 1

The following method is to be used for determining the weighted average of this type. 

• Identify the respective weights of each data entity: Study the table given to you and determine the weight of each data entity. 
• Multiplication step: Multiply a quantity with the weight assigned to it. Perform this for all quantities in the table and store the products. 
• Addition: Add all the products you obtained by multiplying the data entities with their weights. 
• Division: Calculate the total number of terms you are considering while calculating the average. Divide the sum you obtained in the above step by this number. 

Thus, you will have your weighted average. 

Weighted Average Formula

All the above steps can be represented by a simple weight average formula. 

Weighted average = sum of weighted terms/Total number of terms

Here, the sum of weighted terms means the summation of the products of data entities and their weights. 

Weighted Average Example

Calculate the weighted average of marks of a student if students have the following marks and weights for their subjects. 

Science weight = 2

Science marks = 65

Maths’s weight = 3

Maths marks = 70

Social studies weights = 1

Social studies marks = 85

Now, as we know, Weighted average = sum of weighted terms / Total number of terms. 

Hence according to the formula, 

Weighted average = ((2× 65) + (3× 70) + (1×85)) /3

= (130 + 210 + 85) /3

= 141.67 is the weighted average.

Conclusion

Averages are important as they help represent a whole data set with just a single number. Averages are used everywhere. However, there are two types of averages: normal average and weighted average. In weighted average, each data quantity is assigned with the number representing its importance, called the weight.

To find the weighted average of a data set, you first need to multiply each data entity with its respective average, then add all such multiplication products. Finally, divide the answer of about step by the total number of terms. Weighted averages are used in fields like the stock market.