An index number which accounts for the relative importance of the items is known as (i) weighted index (ii) si

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Q. An index number which accounts for the relative importance of the items is known as

(i) weighted index

(ii) simple aggregative index

(iii) simple average of relatives

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Concept understanding — Weighted Price Relative Index

Weighted Price Relative Index – A First Look

Imagine you're tracking how the cost of your monthly shopping basket changes. You buy 10 eggs, 2 litres of milk, and 1 packet of biscuits. If the price of eggs doubles, your total bill goes up a lot. If the price of biscuits doubles, the effect is smaller — because you buy fewer biscuits. A simple average of price changes would treat both items equally, which is misleading. That's where the weighted price relative index comes in.

The Core Idea

A price relative is simply the ratio of the current price of a commodity to its base-year price, usually expressed as a percentage:

\text{Price Relative} = \frac{P_1}{P_0} \times 100

where $P_1$ is the price in the current year and $P_0$ is the price in the base year.

Now, to combine price relatives for multiple commodities, we need to give each commodity its proper importance — its weight. The weight reflects how much of that commodity is consumed or how significant it is in the total expenditure.

The weighted price relative index is then:

I = \frac{\sum (W \times \frac{P_1}{P_0} \times 100)}{\sum W}

where:

$I$ = index number for the current year
$W$ = weight assigned to each commodity
$P_1$ = current year price
$P_0$ = base year price
$\sum$ = sum over all commodities

I = \frac{\sum W \cdot \frac{P_1}{P_0} \times 100}{\sum W}

This is the weighted arithmetic mean of price relatives.

Why the Weighting Matters

Without weights, a 50% rise in the price of salt (which you buy in tiny quantities) would count the same as a 50% rise in the price of rice (which you buy in bulk). That would give a distorted picture of inflation. Weighting corrects this by ensuring that items with greater economic importance have a proportionally larger influence on the index.

The weights are usually based on expenditure patterns from a base-period survey. For example, in a consumer price index, food might get a weight of 50%, housing 20%, transport 10%, and so on. These weights sum to 100 (or 1, depending on how you set them).

A Concrete Example

Suppose in the base year, a family spends ₹200 on wheat and ₹100 on oil. In the current year, wheat costs 1.5 times its base price, and oil costs 2 times its base price.

Commodity	Base Price ( $P_0$ )	Current Price ( $P_1$ )	Price Relative ( $\frac{P_1}{P_0} \times 100$ )	Weight ( $W$ ) – base expenditure	$W \times$ Price Relative
Wheat	₹10/kg	₹15/kg	150	₹200	30,000
Oil	₹100/litre	₹200/litre	200	₹100	20,000
Total				₹300	50,000

The weighted price relative index is:

I = \frac{50,000}{300} = 166.67

This means the overall price level has risen by about 66.67% from the base year. Notice that if you had taken a simple average of the price relatives (150 and 200), you'd get 175 — an overestimate, because the simple average ignores that wheat (with a smaller price rise) had twice the weight of oil.

Where You'll See This

This method is the foundation of most official price indices, including the Consumer Price Index (CPI) and the Wholesale Price Index (WPI) in India. The weights are fixed for a period (say, 5–10 years) based on a comprehensive survey of household consumption or wholesale trade. The index then tracks how the cost of a fixed basket changes over time.

Important

The weighted price relative index is a Laspeyres-type index when base-year quantities are used as weights. It answers the question: "How much more (or less) would the base-year basket cost today?"

A Common Mistake to Avoid

Students often confuse the weight with the price relative. The weight is not the price — it's the importance attached to the commodity, usually based on quantity consumed or expenditure share. The price relative is the pure price change. You multiply them, not add them.

Watch out

Never use current-year quantities as weights in this formula unless you are explicitly computing a Paasche index. The weighted price relative index as taught in Class 11/12 uses base-year weights (quantities or expenditures).

The Big Picture

The weighted price relative index is a tool for measuring the average change in prices while respecting the fact that not all price changes affect us equally. It turns a messy reality — thousands of goods, each with its own price movement — into a single, meaningful number. That number tells you, at a glance, whether your rupee is buying more or less than it used to.

The correct option is (i) weighted index — weights are precisely how an index number reflects the differing importance of items.

Reasoning

A simple (unweighted) index treats every commodity as equally important. But in reality a change in the price of food matters far more to a household than an equal change in the price of a minor item.

To capture this, we attach a weight to each item — usually its share in total expenditure. An index built this way is a weighted index number.

(i) weighted index — accounts for relative importance ✓
(ii) simple aggregative index ✗ — ignores importance
(iii) simple average of relatives ✗ — also unweighted

✓Final answer

(i) weighted index.

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Q.An index number which accounts for the relative importance of the items is known as

Reasoning

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