What is Weighted Average?

S3-SA3-0152

Grade Level:

Class 9

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A Weighted Average is a special type of average where some values contribute more to the final average than others. Instead of treating all values equally, we assign them 'weights' based on their importance or frequency.

Simple Example

Quick Example

Imagine your school marks. If your final exam counts for 50% of your total grade, and your mid-term exam counts for 20%, while homework is 30%, then the final average is a weighted average. The final exam has a higher 'weight' because it's more important.

Worked Example

Step-by-Step

Let's calculate the weighted average marks for a student, Rahul.
Rahul's marks in three subjects are: Maths - 80, Science - 70, English - 90.
--- The school assigns weights: Maths (weight 3), Science (weight 2), English (weight 1).
--- Step 1: Multiply each mark by its weight.
Maths: 80 * 3 = 240
Science: 70 * 2 = 140
English: 90 * 1 = 90
--- Step 2: Add up all these weighted values.
Total weighted sum = 240 + 140 + 90 = 470
--- Step 3: Add up all the weights.
Total weights = 3 + 2 + 1 = 6
--- Step 4: Divide the total weighted sum by the total weights.
Weighted Average = 470 / 6 = 78.33 (approximately)
Answer: Rahul's weighted average mark is approximately 78.33.

Why It Matters

Weighted averages are super important! They help engineers design stronger bridges, economists understand price changes, and even AI algorithms make smarter decisions. Knowing this concept opens doors to careers in data science, finance, and technology, where you'll use it to make sense of complex information.

Common Mistakes

MISTAKE: Forgetting to multiply each value by its weight before summing. | CORRECTION: Always multiply each data point by its corresponding weight first, then sum these products.

MISTAKE: Dividing by the count of items instead of the sum of weights. | CORRECTION: The divisor for a weighted average is always the sum of all the weights, not just how many items there are.

MISTAKE: Treating all weights as equal when they are not specified. | CORRECTION: If weights are given, use them. If no weights are given and all items are equally important, then it's a simple (unweighted) average.

Practice Questions

Try It Yourself

QUESTION: A shop sells 5 kg of rice at Rs 60/kg and 3 kg of rice at Rs 70/kg. What is the weighted average price per kg? | ANSWER: Rs 63.75/kg

QUESTION: Your monthly mobile data usage is: 10 GB (cost Rs 15/GB), 5 GB (cost Rs 20/GB), and 2 GB (cost Rs 25/GB). Calculate your weighted average cost per GB. | ANSWER: Rs 17.5/GB

QUESTION: In a cricket match, a batsman scores 40 runs in 20 balls (strike rate 200), 60 runs in 30 balls (strike rate 200), and 10 runs in 10 balls (strike rate 100). What is his weighted average strike rate, where the 'weight' is the number of balls faced? | ANSWER: 180 runs per 100 balls (or 1.8 runs per ball)

MCQ

Quick Quiz

Which of the following scenarios MOST LIKELY requires a weighted average?

Finding the average height of students in a class.

Calculating the average temperature over a week.

Determining the average price of a stock, where some days have much higher trading volumes.

Calculating the average number of siblings students have.

The Correct Answer Is:

Option C requires a weighted average because trading volume (the 'weight') makes some days' prices more impactful on the overall average than others. The other options typically use a simple average.

Real World Connection

In the Real World

When you check the 'overall rating' of a product on Amazon or Flipkart, it's often a weighted average. The ratings from 'verified purchasers' or more recent reviews might be given higher weight to give you a more accurate picture. Even in finance, stock market indices like the Sensex use weighted averages based on company market values.

Key Vocabulary

Key Terms

AVERAGE: A single value that represents the typical or central value of a set of numbers. | WEIGHT: A measure of the importance or frequency of a particular value in a dataset. | DATASET: A collection of related data. | SUM: The result of adding two or more numbers.

What's Next

What to Learn Next

Great job understanding weighted averages! Next, you can explore 'Mean, Median, and Mode' to see how different types of averages are used. This will deepen your understanding of how to analyze data effectively and pick the right average for different situations.