A price index compares a price now with the price in a base year, where the base year is set to 100. The formula is I = (Q₁ ÷ Q₀) × 100, with Q₁ the current price and Q₀ the base price.
This lesson starts the index numbers chapter. The next lesson, combining weighted indices, uses the same formula once per item.
What does the formula say?
Divide the price now by the price in the base year, then multiply by 100. The base year always has an index of exactly 100, because Q₁ and Q₀ are then the same.
An index above 100 means the price has risen since the base year. An index below 100 means it has fallen.
Worked example: three questions from one formula
A packet of rice cost RM8.00 in 2020 (the base year) and RM9.20 in 2024.
Find the index. I = (9.20 ÷ 8.00) × 100 = 1.15 × 100 = 115. That means a 15% rise since 2020, not a 115% rise.
Find the current price from an index. A tin of cooking oil cost RM4.80 in 2020 and its index in 2024 is 125. Current price = (125 ÷ 100) × 4.80 = 1.25 × 4.80 = RM6.00.
Find the base price. A bag of flour costs RM13.50 in 2024 and its index is 112.5 (base 2020). Base price = 13.50 ÷ 1.125 = RM12.00. Check: (13.50 ÷ 12.00) × 100 = 112.5.
The mistake that costs marks
The common slip is to put the base price on top. For the rice, that gives (8.00 ÷ 9.20) × 100 = 86.96, an index below 100, even though the price clearly rose.
A quick sense check catches it: if the price went up, the index must be above 100. If your answer says otherwise, the two prices are the wrong way round.
| Check | Wrong setup | Right setup |
|---|---|---|
| Top of the fraction | 8.00 (base) | 9.20 (this year) |
| Result | 86.96 | 115 |
| Sense check | Below 100 after a rise | Above 100 after a rise |
Check yourself
Cooking oil cost RM5.50 in 2019. Its index in 2023 is 120 with 2019 as the base year. Find its price in 2023. Then find the 2023 index for eggs that cost RM10.00 in 2019 and RM9.00 in 2023.
Answer
Price in 2023 = (120 ÷ 100) × 5.50 = 1.2 × 5.50 = RM6.60.
Egg index = (9.00 ÷ 10.00) × 100 = 90. Below 100 matches the fall in price, a 10% decrease.
What to study next
Move on to combining weighted indices, then test yourself with the index numbers practice set. The word-problem structure worksheet helps you lay out a wordy question before calculating.
If you want a teacher to watch your setup, see online one-to-one Additional Mathematics tuition.