Percentage Change

Percentage change questions are among the most frequently tested in QR. They ask you to calculate how much a value has increased or decreased as a proportion of the original value. This lesson covers calculating percentage increases and decreases, comparing percentage changes, and avoiding the common traps.

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The Formula

Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100

If the result is positive, it is an increase. If negative, it is a decrease.

Simplified:

Percentage Change = (Change ÷ Original) × 100

Critical Rule: Always divide by the original value (the "before" value, the starting point). This is the single most important thing to remember about percentage change.

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Calculating Percentage Increase

Worked Example

Data: A town's population grew from 25,000 to 28,500.

Question: What is the percentage increase?

• Change: 28,500 − 25,000 = 3,500
• Percentage increase: (3,500 ÷ 25,000) × 100
• 3,500 ÷ 25,000 = 0.14
• 0.14 × 100 = 14%

Simplification Shortcut

When possible, simplify the fraction before dividing:

• 3,500/25,000 = 35/250 = 7/50 = 14/100 = 14%

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Calculating Percentage Decrease

Worked Example

Data: Sales fell from 1,200 units to 900 units.

Question: What is the percentage decrease?

• Change: 1,200 − 900 = 300
• Percentage decrease: (300 ÷ 1,200) × 100
• 300/1,200 = 1/4 = 0.25
• 0.25 × 100 = 25% decrease

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Comparing Percentage Changes

A very common QR question: "Which category had the greatest percentage change?"

Why Absolute Changes Are Not Enough

Product	2023 Sales	2024 Sales	Absolute Change	Percentage Change
A	500	600	+100	+20%
B	200	280	+80	+40%
C	1,000	1,080	+80	+8%

Products B and C both increased by 80 units, but B's percentage change (40%) is five times C's (8%) because B started from a much lower base.

Always read the question carefully: Does it ask for the greatest absolute change or the greatest percentage change?

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Expressing Change as a Percentage

Sometimes you are given two values and must express the difference as a percentage of a specific reference value.

"As a Percentage of the Original"

Standard percentage change — divide by the original value.

Example: Temperature rose from 15°C to 18°C.

Change as a percentage of the original: (3 ÷ 15) × 100 = 20%

"As a Percentage of the New Value"

Sometimes questions ask for the difference as a percentage of the new value.

Example: "The new price is how much higher than the old price, as a percentage of the new price?"

Old = £80, New = £100.

Change as a percentage of the new: (20 ÷ 100) × 100 = 20%

Change as a percentage of the old: (20 ÷ 80) × 100 = 25%

These give different answers. Read the question!

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Percentage Points vs Percentage Change

This is a subtle but testable distinction.

Example: A pass rate increases from 60% to 75%.

• Increase in percentage points: 75% − 60% = 15 percentage points
• Percentage increase: ((75 − 60) ÷ 60) × 100 = (15 ÷ 60) × 100 = 25%