Introduction to Index Numbers

Have you ever heard your grandparents talk about how a loaf of bread used to cost just a few pennies? Over time, prices change, and the value of money shifts. In Statistics, we use Index Numbers to track these changes clearly. Instead of looking at messy raw data, index numbers allow us to compare values from different years against a starting point, making it easy to see trends at a glance.

In this chapter, we will focus on the standard index number formula and three very important real-world examples: RPI, CPI, and GDP.

Note: If you are a Higher Tier student, you will build on these basics in the next chapter covering weighted and chain base index numbers.

The Index Number Formula

An index number is essentially a way of showing a value as a percentage of a base year value. The base year is the reference point we choose to start from.

To calculate an index number, use this formula (which you need to memorise!):

\( \text{Index number} = \frac{\text{current value of item}}{\text{value in base year}} \times 100 \)

How it works step-by-step:

1. Identify the Base Year: This is the year we are comparing everything back to. The index number for the base year is always 100.
2. Divide: Take the price or value of the item in the year you are interested in and divide it by the value it had in the base year.
3. Multiply by 100: This turns the ratio into an index number.

Example: In 2015 (Base Year), a train ticket cost \( £20 \). In 2024, the same ticket costs \( £25 \).
\( \text{Index Number} = \frac{25}{20} \times 100 = 1.25 \times 100 = 125 \)
This means the price is now 125% of what it was in 2015, or a 25% increase.

Quick Review: If an index number is 110, the value has increased by 10%. If it is 95, the value has decreased by 5%.

Three Key Measures: RPI, CPI and GDP

The government and economists use specific index numbers to keep track of the UK economy. You need to know what these three acronyms stand for and what they measure.

1. Retail Price Index (RPI)

The RPI measures the change in the cost of a "basket" of everyday retail goods and services. It includes things like food, clothing, and petrol. Importantly, the RPI includes housing costs, such as mortgage interest payments and council tax.

2. Consumer Price Index (CPI)

The CPI is the official measure of inflation in the UK. Like the RPI, it tracks a basket of goods, but it is calculated differently and excludes most housing costs (like mortgage payments). Because it is used across Europe, it allows us to compare UK inflation with other countries easily.

3. Gross Domestic Product (GDP)

While RPI and CPI look at prices, GDP looks at the "size" of the economy. It is an index that measures the total value of all goods and services produced within a country over a specific time.

  • If the GDP index is rising, the economy is growing.
  • If the GDP index is falling, the economy is shrinking.

Key Takeaway Table

RPI: Retail prices including housing costs.
CPI: Retail prices excluding most housing costs (official inflation measure).
GDP: Total value of a country's production (economic growth).

Interpreting Index Numbers in Context

When you see a table of index numbers in your exam, you aren't just looking for the biggest number; you are looking for the rate of change.

Example Table:
Year 1 (Base): 100
Year 2: 104
Year 3: 107
Year 4: 106

Interpretation:
- Between Year 1 and Year 2, prices rose by 4%.
- Between Year 2 and Year 3, prices continued to rise, but the total increase since the base year is now 7%.
- In Year 4, the index dropped to 106. This means prices decreased compared to Year 3, but they are still 6% higher than the base year.

Don't worry if this seems tricky! Just remember: an index number over 100 means an increase from the base year, and under 100 means a decrease.

Common Mistakes to Avoid

1. Mixing up the numerator and denominator: Always put the Base Year value on the bottom of the fraction.
2. Forgetting to multiply by 100: Without this step, you just have a decimal, not an index number.
3. Thinking 110 means a 110% increase: An index of 110 means the price is 110% of the original, which is a 10% increase. Always subtract 100 to find the percentage change.

Quick Review Quiz

1. What is the index number for any base year? (Answer: 100)
2. Does CPI include mortgage interest payments? (Answer: No, RPI usually does)
3. If a GDP index changes from 100 to 102, did the economy grow or shrink? (Answer: Grow)

Summary Tip: Index numbers are just a way to make big, complicated numbers easier to compare. Use the formula, identify your base year, and you'll be able to tackle any question on this topic!