Introduction To Weighted Average

We will learn a new concept in average today, which is called the $Weighted\ Average$.

Let us say we have a group of numbers, where some of the numbers are repeated. Then what is the average of these numbers?

We will take an example to understand this. Let us some kids bought candies at a candy store. $10$ kids bought $40$ candies each, and $5$ kids bought $70$ candies each. What is the average number of candies bought by each kid?

The sum of all the candy bars bought by all students $= 10 \times 40 + 5 \times 70 = 400 + 350 = 150$

The total number of kids $= 10 + 5$

The average number of candies bought by each kid $= 750 \div 15 = 50$ gms

Here we can see that the value $40$ occurred $10$ times and the value $70$ occurred $5$ times.

Here $10$ is called the weightage (also the frequency) for the value of $40$ and $5$ is the weightage of the value $70$.

We can calculate the weighted average using $weighted\ average = \dfrac{sum\ of\ (weight \times value)}{sum\ of\ weights}$

We will see one more example of this.

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In an exam of $100$ marks $15$ students scored $84$ each, $12$ students scored $75$ each, $8$ students scored $85$ each, $5$ students scored $96$ each.

What is the average score of of the class?

Here, since we are finding the average score, the score is the value and the number of students is the weightage.

The average score of the class $= \dfrac{15 \times 84 + 12 \times 75 + 8 \times 85 + 5 \times 96}{15 + 12 + 8 + 5} = \dfrac{3320}{40} = 83$