What is Weighted Mean?

S3-SA3-0332

Grade Level:

Class 9

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

Definition

What is it?

The Weighted Mean 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 'weights' to show their importance.

Simple Example

Quick Example

Imagine your school calculates final marks. If your End-Term exam counts for 60% of your grade and your Mid-Term exam counts for 40%, the End-Term exam has a higher 'weight'. To find your final mark, you'd use a weighted mean.

Worked Example

Step-by-Step

Let's find the weighted average cost of chai.
---You bought 2 cups of chai at ₹15 each.
---You then bought 3 cups of chai at ₹20 each.
---The 'values' are the prices (₹15, ₹20) and the 'weights' are the number of cups (2, 3).
---Step 1: Multiply each value by its weight: (₹15 * 2) = ₹30 and (₹20 * 3) = ₹60.
---Step 2: Add these products: ₹30 + ₹60 = ₹90.
---Step 3: Add all the weights: 2 + 3 = 5.
---Step 4: Divide the sum of products by the sum of weights: ₹90 / 5 = ₹18.
---The weighted average cost per cup of chai is ₹18.

Why It Matters

Understanding weighted mean is super useful! Data scientists use it to make sense of complex information, like predicting cricket match outcomes. Engineers use it to balance different factors in design, and in AI, it helps train smart systems. It's a foundational tool for many exciting future careers!

Common Mistakes

MISTAKE: Simply adding all values and dividing by the count, like a simple average. | CORRECTION: Remember to multiply each value by its weight BEFORE adding them up.

MISTAKE: Forgetting to sum the weights in the denominator. | CORRECTION: Always divide the sum of (value * weight) by the sum of ALL the weights.

MISTAKE: Confusing the 'value' with the 'weight'. | CORRECTION: Identify what you are averaging (the value) and how important each one is (the weight). For example, marks are values, percentages are weights.

Practice Questions

Try It Yourself

QUESTION: A shop sells two types of sweets: 5 laddus at ₹10 each and 3 gulab jamuns at ₹12 each. What is the weighted average price per sweet? | ANSWER: ₹10.75

QUESTION: In a school project, the research part counts for 40% (score 80), and the presentation part counts for 60% (score 90). What is the student's weighted average score for the project? | ANSWER: 86

QUESTION: A bus travels 10 km at 40 km/h and then 20 km at 60 km/h. What is the weighted average speed of the bus? (Hint: Time is the weight, and Time = Distance/Speed) | ANSWER: 51.43 km/h (approx)

MCQ

Quick Quiz

Which of the following scenarios would MOST likely require calculating a weighted mean?

Finding the average height of all students in a class.

Calculating the average temperature over a week where daily temperatures are equal.

Determining the average price of a mobile phone where different models contribute differently to total sales.

Finding the average number of runs scored by a cricket team in 5 matches.

The Correct Answer Is:

Option C requires a weighted mean because different mobile phone models (values) might have different sales volumes (weights), making some prices more impactful on the average. Other options describe simple averages.

Real World Connection

In the Real World

When you see product ratings on e-commerce apps like Flipkart or Amazon, often the 'average rating' is a weighted mean. Reviews from verified buyers or more recent reviews might be given more 'weight' to ensure the average truly reflects current customer satisfaction.

Key Vocabulary

Key Terms

AVERAGE: A single value that represents a set of values | WEIGHT: A measure of importance or frequency assigned to a value | MEAN: Another term for average | DATA: Facts and statistics collected together for reference or analysis

What's Next

What to Learn Next

Great job understanding Weighted Mean! Next, explore 'Measures of Central Tendency' like Median and Mode. These concepts will further deepen your understanding of how to analyze and interpret data, which is crucial for higher studies in many fields.