What is a Weighted Index Number?

S7-SA3-0170

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

A Weighted Index Number is a special type of average that gives different importance (or 'weight') to different items when calculating a change over time. Instead of treating all items equally, it considers how much each item contributes to the overall picture.

Simple Example

Quick Example

Imagine you're calculating your average marks. If your Science exam counts for twice as much as your Art exam, you wouldn't just add them up and divide by two. You'd give Science more 'weight' in the calculation, just like a weighted index number does.

Worked Example

Step-by-Step

Let's calculate a weighted average price index for chai ingredients.

Items: Tea Leaves, Sugar, Milk

Step 1: Note down current prices and base year prices for each item.
Tea Leaves: Current = Rs 100/kg, Base = Rs 80/kg
Sugar: Current = Rs 45/kg, Base = Rs 40/kg
Milk: Current = Rs 60/litre, Base = Rs 50/litre

Step 2: Assign weights based on how much you use. (Let's say Tea Leaves: 3, Sugar: 2, Milk: 5)

Step 3: Calculate the price relative for each item (Current Price / Base Price) * 100.
Tea Leaves: (100 / 80) * 100 = 125
Sugar: (45 / 40) * 100 = 112.5
Milk: (60 / 50) * 100 = 120

Step 4: Multiply each price relative by its weight.
Tea Leaves: 125 * 3 = 375
Sugar: 112.5 * 2 = 225
Milk: 120 * 5 = 600

Step 5: Sum these weighted price relatives: 375 + 225 + 600 = 1200

Step 6: Sum the total weights: 3 + 2 + 5 = 10

Step 7: Divide the sum of weighted price relatives by the sum of weights.
Weighted Index Number = 1200 / 10 = 120

Answer: The Weighted Index Number is 120.

Why It Matters

Weighted index numbers are super important in economics and finance, helping us understand inflation or stock market changes accurately. Doctors use them to assess health risks, and engineers use them to evaluate material performance, making them valuable tools for careers in AI, FinTech, and even medicine.

Common Mistakes

MISTAKE: Treating all items equally when they have different importance. | CORRECTION: Always identify the 'weights' or importance of each item before calculation.

MISTAKE: Forgetting to multiply the price relative by its weight. | CORRECTION: The formula requires multiplying each item's price relative by its assigned weight before summing them up.

MISTAKE: Dividing by the number of items instead of the sum of weights. | CORRECTION: For a weighted index, you must divide the sum of (weighted price relatives) by the sum of all the weights.

Practice Questions

Try It Yourself

QUESTION: Calculate the weighted index if item A has a price relative of 110 and weight 4, and item B has a price relative of 120 and weight 6. | ANSWER: (110*4 + 120*6) / (4+6) = (440 + 720) / 10 = 1160 / 10 = 116

QUESTION: A family's monthly budget items are Food (weight 5, price relative 105), Rent (weight 4, price relative 102), and Transport (weight 1, price relative 115). What is the weighted average price index for their expenses? | ANSWER: (5*105 + 4*102 + 1*115) / (5+4+1) = (525 + 408 + 115) / 10 = 1048 / 10 = 104.8

QUESTION: Suppose an investor has 3 stocks: Stock X (Price Relative 108, Weight 25%), Stock Y (Price Relative 115, Weight 40%), and Stock Z (Price Relative 100, Weight 35%). Calculate the weighted index for their portfolio. | ANSWER: (108*25 + 115*40 + 100*35) / (25+40+35) = (2700 + 4600 + 3500) / 100 = 10800 / 100 = 108

MCQ

Quick Quiz

Which of the following best describes the purpose of 'weights' in a Weighted Index Number?

To make the calculation simpler

To give more importance to certain items

To always increase the final index value

To remove items that are not important

The Correct Answer Is:

Weights are used to reflect the relative importance or contribution of different items to the overall index, ensuring a more accurate representation of change.

Real World Connection

In the Real World

In India, the 'Consumer Price Index (CPI)' is a famous weighted index number. It tracks the average change in prices of goods and services consumed by households. The government uses it to understand inflation, impacting policies that affect your parents' salaries and the cost of everyday items like groceries and petrol.

Key Vocabulary

Key Terms

WEIGHT: The importance or significance given to an item in a calculation. | INDEX NUMBER: A statistical measure showing changes in a variable over time. | PRICE RELATIVE: The ratio of the current price to the base price, usually multiplied by 100. | BASE YEAR: The reference year against which changes are measured. | INFLATION: The rate at which the general level of prices for goods and services is rising.

What's Next

What to Learn Next

Great job understanding Weighted Index Numbers! Next, you can explore different types of weighted index numbers like Laspeyres' and Paasche's Index. These build on what you've learned by showing how different weighting methods can lead to slightly different insights, which is super useful in economics!