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Economics · 01 / 06

Indicators: rates, indices, charts

High school foundations · Worked example and 4 exercises with solutions, at your pace.

Need a foundation?Fractions: share the same wholeProportionality and percentages
UnderstandSee an exampleGuided exercise3 progressive challenges

The principle, simply

An absolute change uses the original unit; a percentage change compares it with the initial value. A base-100 index compares values with a reference. Differences between percentage rates use percentage points. Inspect dates, scope, source and axes; truncated axes may visually exaggerate change.

t=(V_1-V_0)/V_0*100
THE PICTURE TO REMEMBERIndicators: rates, indices, charts
  1. 01Initial value
  2. 02Difference
  3. 03Ratio to start
  4. 04Unit and interpretation

WORKED EXAMPLE

From principle to reasoning

80 to 100 is +20 units, +25%, index 125. A rate moving from 20% to 25% rises five points and 25% relatively.

Solve a problem in this subject

  1. Define the indicator

    Specify quantity, population, period and unit. Distinguish level, change, rate of change and percentage points.

  2. Read or calculate

    Identify denominator and comparison base. From 20% to 25% is +5 percentage points but a 25% relative increase.

  3. Explain a mechanism

    Show steps connecting a proposed cause to its effect. Separate model, assumptions and evidence; correlation alone is insufficient.

  4. Discuss with evidence

    Use a precise example and limitations. Averages conceal distributions; nominal measures include price effects.

YOUR TURN

01 · Try before checking

Find the percentage change from 200 to 180.

One hint

Divide the difference by the initial value.

Reveal and understand the solution

(180 − 200)/200 × 100 = −10%; base-100 index 90.

Compare method, conditions and answer; identify the exact part to revisit.

IMPROVE THROUGH PRACTICE

Three additional challenges with solutions

Start with the first challenge. Write your method before opening a hint; use the solution to find the first step that needs work.

Reflect after practising
02 · Recognise and understandLink to this exercise

An indicator rises from 200 to 230. Find percentage change.

A hint to get started

Use the initial value as the base.

Step-by-step solution
  1. (230 − 200)/200 = 0.15.
  2. The rate is 15%.
  3. The absolute increase of 30 is not a rate.

Which step did you miss? Retry without help, then explain why the method works.

03 · Apply the methodLink to this exercise

A share rises from 20% to 25%. Find percentage points and relative change.

A hint to get started

A percentage point differs from percentage change.

Step-by-step solution
  1. Difference: 25 − 20 = 5 points.
  2. Relative change: 5/20 = 25%.
  3. Specify which measure the question requires.

Which step did you miss? Retry without help, then explain why the method works.

04 · Go furtherLink to this exercise

An index is 120 then 126. Find the change between those dates.

A hint to get started

Use 120, not 100, as the denominator.

Step-by-step solution
  1. (126 − 120)/120 = 0.05.
  2. The rise is 5%.
  3. Six index points do not mean a 6% rise.

Which step did you miss? Retry without help, then explain why the method works.

The trap to avoid

Use the starting denominator and distinguish points from percent.

Without notes, can you…

  • Explain the principle in your own words?
  • Rebuild the diagram and its connections?
  • Solve the exercise and justify the method?

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