Management Accounting · Summarising and analysing data

Index Numbers: Weighted Indices, Laspeyres vs Paasche and Deflating

Updated 11 October 2026 · Fact-checked

An index number shows how a price, quantity or value changes compared with a base period set at 100. To solve questions, divide the current figure by the base figure and multiply by 100. For weighted indices, multiply each item by a weight first. To deflate, divide the value by the price index and multiply by 100.

Understand Index Numbers

An index number measures change over time. You pick a base period and set its value to 100. Every other period is shown relative to it. An index of 125 means the figure is 25% higher than in the base period. An index of 90 means it is 10% lower.

A simple index tracks one item, such as the price of one material. Divide the current price by the base price and multiply by 100. It is easy, but a business buys many items, and a single price tells you little about overall cost changes.

A weighted index combines many items. Each item gets a weight showing its importance, such as the quantity bought or the amount spent. Without weights, a tiny item would count as much as the biggest one. Weights make the index realistic.

Two weighted price indices are tested. Laspeyres uses base-period quantities as weights. Paasche uses current-period quantities. Laspeyres is cheaper and easier to produce because the weights never change. But as buying patterns shift, the base weights go out of date, and Laspeyres tends to overstate price rises when people switch away from items that rose most. Paasche reflects current buying patterns but needs new quantity data every period.

Indices are also used to deflate values. Money figures rise with inflation, so a rise in sales revenue may not mean more goods were sold. Dividing the value by a price index removes the price effect and gives a figure in base-period prices, called a real or constant-price figure.

Key formulas to remember

Simple price index: Price index = (Current price ÷ Base price) × 100; Works the same for quantity or any other single series.
Laspeyres price index: Σ(P1 × Q0) ÷ Σ(P0 × Q0) × 100; P0 and P1 are base and current prices. Q0 is base-period quantity. Weights stay fixed.
Paasche price index: Σ(P1 × Q1) ÷ Σ(P0 × Q1) × 100; Q1 is current-period quantity. Weights change each period.
Laspeyres quantity index: Σ(Q1 × P0) ÷ Σ(Q0 × P0) × 100; Quantities change, prices held at base. Paasche quantity index uses current prices: Σ(Q1 × P1) ÷ Σ(Q0 × P1) × 100.
Deflating a value: Real value = Current value ÷ Price index × 100; Gives the value in base-period prices.
Rate of change between periods: % change = (Index later − Index earlier) ÷ Index earlier × 100; Do not simply subtract index points unless the earlier index is 100.
Changing the base: New index = Old index ÷ Old index of new base period × 100; The new base year then shows 100.

How to solve Index Numbers questions

Use this method for any index number question, whether it asks for an index, a weighted index or a deflated value.

1Read the question and identify what you must find: price index, quantity index, deflated value or percentage change.
2Find the base period. Its index is 100. Check which year is the base before you start.
3Decide if the index is simple or weighted. If several items are involved, it is weighted.
4For a weighted index, pick the weights: base quantities for Laspeyres, current quantities for Paasche. For a quantity index, hold prices constant instead.
5Calculate the top and bottom lines separately. Write each total down before dividing.
6Divide, multiply by 100, and round as the question instructs.
7To deflate, divide the money value by the index and multiply by 100. To find a percentage change, use the index values, not the raw points.
8Check the answer is sensible. Rising prices should give an index above 100.

Quickest way: Fast Laspeyres or Paasche check

When to use it: Use when a Section A question gives a small table of prices and quantities and asks for a weighted index.

Underline whether the weights are base or current quantities.
Build only two columns of totals: current prices times the chosen quantity, and base prices times the same quantity.
Divide the first total by the second and multiply by 100.
For deflating, rewrite as value ÷ index × 100 and use your calculator memory.
Eliminate options: a price rise means the answer must exceed 100.

Common mistakes in Index Numbers

Mixing quantities from different periods, for example using Q1 in the top line and Q0 in the bottom line.
Students rush and forget that both lines use the same weights.
Fix: Write Q0 or Q1 at the top of your working and use only that quantity in both lines.
Swapping Laspeyres and Paasche.
The names are easy to confuse.
Fix: Remember: Laspeyres starts with L for Last, meaning the base year quantities fixed at the start. Paasche uses the present quantities.
Multiplying instead of dividing when deflating.
Students think of the index as a growth factor to apply.
Fix: To remove inflation, divide the value by the index and multiply by 100 (that is, divide by index ÷ 100). The deflated figure should be lower when prices have risen.
Calculating percentage change by subtracting index points when the earlier index is not 100.
Index 120 to 150 looks like a 30% rise.
Fix: Use (150 − 120) ÷ 120 × 100 = 25%.
Forgetting to multiply by 100 or giving the answer as a decimal.
The division step feels like the end.
Fix: Index answers are on a base of 100. Check your answer is near 100.

Worked examples

Example 1

A business buys two materials. Base year prices and quantities: X $4 per kg, 100 kg; Y $10 per kg, 50 kg. Current year: X $5 per kg, 120 kg; Y $12 per kg, 40 kg. Calculate the Laspeyres and Paasche price indices.

Show the solution

Laspeyres uses base quantities (Q0): X 100, Y 50.
Top line: (5 × 100) + (12 × 50) = 500 + 600 = 1,100.
Bottom line: (4 × 100) + (10 × 50) = 400 + 500 = 900.
Laspeyres = 1,100 ÷ 900 × 100 = 122.2.
Paasche uses current quantities (Q1): X 120, Y 40.
Top line: (5 × 120) + (12 × 40) = 600 + 480 = 1,080.
Bottom line: (4 × 120) + (10 × 40) = 480 + 400 = 880.
Paasche = 1,080 ÷ 880 × 100 = 122.7.

Answer: Laspeyres price index = 122.2; Paasche price index = 122.7.

Example 2

A company's sales revenue was $240,000 in Year 1 and $297,000 in Year 2. The relevant price index was 100 in Year 1 and 110 in Year 2. Calculate the real percentage change in sales between the two years, at Year 1 prices.

Show the solution

Deflate Year 2 revenue: 297,000 ÷ 110 × 100 = 270,000.
Year 1 revenue is already at base prices: 240,000.
Real change = 270,000 − 240,000 = 30,000.
Percentage change = 30,000 ÷ 240,000 × 100 = 12.5%.
Check: Money sales rose 23.75% (57,000 ÷ 240,000), but prices rose 10%, so the real rise is smaller at 12.5%.

Answer: Real sales rose by 12.5% at Year 1 prices (deflated Year 2 sales were $270,000).

Exam tips

Read the weights carefully. The words base year quantities or current year quantities decide Laspeyres or Paasche.
In number entry questions, check the rounding instruction, such as one decimal place, before you type.
For multiple response questions on Laspeyres versus Paasche, remember: Laspeyres needs less data but can overstate price rises; Paasche needs current quantities each period.
Sanity check every deflated answer. If prices rose, the real value must be lower than the money value.
Write down the base year first. Many errors come from using the wrong year as 100.

Practice questions from Summarising and analysing data

Index Numbers in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Index Numbers: frequently asked questions

What is the difference between Laspeyres and Paasche indices?

Laspeyres weights prices by base-period quantities. Paasche weights them by current-period quantities. Laspeyres is simpler because weights stay fixed, while Paasche is more up to date but needs new quantity data each period.

How do I deflate figures using an index number?

Divide the money value by the price index and multiply by 100. This gives the value at base-period prices, which lets you compare real changes in volume across years.

What does an index of 100 mean?

It marks the base period. Every other index shows the figure as a percentage of the base value. An index of 130 means 30% higher than the base.

How do I calculate a weighted price index?

Choose weights, usually quantities. Multiply current prices by the weights and add them up. Do the same with base prices. Divide the first total by the second and multiply by 100.