E10b — AQA GCSE Statistics

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E10b exam tips

Quick Revision Summary (Key Takeaway)

E10b in AQA GCSE Statistics covers the use of index numbers to track changes in variables such as prices, quantities, or values over time, typically expressed relative to a base year of 100. Students must calculate simple and weighted index numbers, interpret them in context, and use them to compare changes across different categories or time periods.

Topic Overview

Index numbers are a statistical tool used to measure and compare changes in a variable over time, such as prices, wages, or production levels. In AQA GCSE Statistics, you learn to calculate simple index numbers relative to a base year (usually set to 100) and weighted index numbers that account for the relative importance of different items in a basket. This topic is essential for understanding economic indicators like inflation and for making fair comparisons across different time periods or regions.

E10b specifically focuses on the calculation and interpretation of index numbers, including the use of the Retail Prices Index (RPI) and other weighted indices. It builds on your understanding of percentages and ratios, and it connects to other statistical topics such as time series and data presentation. Mastering index numbers allows you to analyse real-world data critically, a skill that is valuable in further study and everyday life.

Key Concepts

→An index number expresses a value as a percentage of a base value, with the base year typically set to 100. A value above 100 indicates an increase; below 100 indicates a decrease.
→Simple index numbers compare a single item over time, while weighted index numbers combine multiple items, each multiplied by a weight reflecting its importance.
→The formula for a simple index is: Index = (value in current period / value in base period) x 100.
→Weighted index numbers are calculated by summing the products of current prices and weights, dividing by the sum of base prices and weights, then multiplying by 100.
→Index numbers allow comparisons across different scales and are widely used in economics, such as the Consumer Prices Index (CPI) and RPI.

Examiner Tips

💡Always state the base year and write the formula before substituting values. This secures method marks even if arithmetic errors occur.
💡When interpreting an index, relate it back to the base year: 'An index of 120 means a 20% increase since the base year.' Avoid vague statements like 'it went up'.
💡For weighted indices, show how you calculate the weighted totals (price x weight) for both years. This demonstrates understanding and earns full marks.

Common Mistakes

Students often think an index of 150 means the value has increased by 150%. Correction: It means a 50% increase, because the base is 100.
Students sometimes forget to multiply by 100, leaving the index as a decimal or fraction. Correction: Always multiply by 100 to express the index relative to 100.
When using weighted indices, students may ignore the weights and treat all items equally. Correction: Weights reflect relative importance; items with larger weights have a greater impact on the index.

Revision Plan

1Day 1-2: Revise the basic formula for simple index numbers. Practice calculating indices for single items using past paper questions.
2Day 3-4: Learn how to interpret index numbers in context. Write explanations for given index values, focusing on the base year and percentage change.
3Day 5-6: Study weighted index numbers. Understand how to apply weights and calculate weighted totals. Practice with a basket of goods example.
4Day 7-8: Work through exam-style questions on both simple and weighted indices, including those that require interpretation and comparison.
5Day 9-10: Review common mistakes and examiner tips. Create a summary sheet with formulas and key points, then test yourself with active recall.

Exam Question Types

📋Calculation of a simple index number from given data. Advice: Show the formula, substitute correctly, and round appropriately if required.
📋Interpretation of an index number in a real-world context (e.g., 'What does an index of 115 mean?'). Advice: Always mention the base year and the percentage change.
📋Calculation of a weighted index number using a table of prices and weights. Advice: Calculate weighted totals for each year, sum them, then apply the formula.
📋Comparison of two index numbers or time periods. Advice: Comment on which has increased more and by what percentage, using the index values.

Command Word Expectations (AQA)

Calculate

You must show a clear method, substitute values into the correct formula, and perform the arithmetic accurately. A numerical answer is required, often with units or an index value.

Interpret

You must explain what the index number means in the context of the question, referring to the base year and the percentage change. Use phrases like 'increased by X%' or 'is X% higher than'.

Compare

You must identify similarities and differences between two or more index numbers or time periods, using numerical values to support your statements. For example, 'The index for 2020 is higher than for 2010, indicating a greater increase.'

How Students Lose Marks (Examiner Pitfalls)

Pitfall: Forgetting to multiply by 100 when calculating an index number, or using the wrong base year. Students often divide the current value by the base value but leave the result as a decimal instead of converting to an index.

❌ Weak Answer (Loses Marks):Index = 45 / 30 = 1.5, so the index is 1.5.

Example improved answer:Index number = (value in current year / value in base year) x 100 = (45 / 30) x 100 = 150. This means the value has increased by 50% since the base year.

Examiner Tip: Always write the formula first, substitute clearly, and remember that an index of 100 represents no change from the base year. State the base year explicitly in your answer.

Pitfall: Misinterpreting a weighted index number, such as the Retail Prices Index (RPI), by treating it as a simple average of individual price changes rather than accounting for different weights. Students also lose marks by not explaining what the index value means in real terms.

❌ Weak Answer (Loses Marks):The RPI is 120, so prices have gone up by 20% for everything.

Example improved answer:An RPI of 120 means that the weighted average of prices in the current year is 20% higher than in the base year. This does not mean every item increased by 20%; items with higher weights have a greater influence on the index.

Examiner Tip: When interpreting a weighted index, always refer to the weights and explain that the index represents a weighted average. Use phrases like 'on average, taking into account the relative importance of each item'.

Step-by-Step Worked Solutions

Question: The price of a loaf of bread was 1.20 in 2015 and 1.50 in 2020. Calculate the index number for the price of bread in 2020 using 2015 as the base year. Interpret your result.

1.Step 1: Identify the base year value (2015) = 1.20 and the current year value (2020) = 1.50.
2.Step 2: Apply the index number formula: Index = (current value / base value) x 100 = (1.50 / 1.20) x 100.
3.Step 3: Calculate: 1.50 / 1.20 = 1.25, then 1.25 x 100 = 125.
4.Step 4: Interpret: An index of 125 means the price in 2020 is 25% higher than in 2015.

Final Answer: Index number = 125. The price of bread increased by 25% between 2015 and 2020.

Question: A student calculates a weighted index for a basket of goods. The base year total weighted cost is 400. In the current year, the total weighted cost is 460. Calculate the weighted index and explain what it shows.

1.Step 1: Identify the base year total weighted cost = 400 and current year total weighted cost = 460.
2.Step 2: Use the weighted index formula: Weighted index = (current total weighted cost / base total weighted cost) x 100.
3.Step 3: Substitute: (460 / 400) x 100 = 1.15 x 100 = 115.
4.Step 4: Interpret: A weighted index of 115 means the overall weighted cost of the basket has increased by 15% since the base year.

Final Answer: Weighted index = 115. The basket of goods costs 15% more than in the base year, taking into account the weights of each item.

Active Recall Memory Test

What is the formula for a simple index number?

Key Fact: Index = (value in current period / value in base period) x 100.

What does an index number of 100 represent?

Key Fact: An index of 100 means there has been no change from the base year; the value is the same as the base value.

How do you calculate a weighted index number?

Key Fact: Multiply each item's price by its weight, sum these for both the current and base years, then divide the current total by the base total and multiply by 100.

What does an index number of 85 indicate?

Key Fact: An index of 85 means the value has decreased by 15% compared to the base year.

Frequently Asked Questions

What is an index number in statistics?

An index number is a statistical measure that expresses the change in a variable over time relative to a base value, which is usually set to 100. It allows you to compare values from different time periods easily. For example, if the price of an item was 2 in the base year and 3 now, the index is 150, meaning a 50% increase.

How do I calculate a weighted index number?

To calculate a weighted index, you first multiply each item's price by its weight for both the base year and the current year. Then you sum these weighted values for each year. Finally, divide the current year total by the base year total and multiply by 100. This gives an index that accounts for the relative importance of each item.

What does an index of 120 mean?

An index of 120 means that the value in the current period is 20% higher than in the base period. It does not mean a 120% increase; the base is 100, so 120 represents a 20% rise. Always relate the index back to the base year when interpreting.

Why do we use index numbers?

Index numbers are used to simplify comparisons of data over time, especially when values are on different scales or when we want to track changes in a basket of goods. They are essential in economics for measuring inflation, such as the Retail Prices Index (RPI). They also allow fair comparisons by removing the effect of the base year's absolute values.

What is the difference between a simple index and a weighted index?

A simple index number tracks the change in a single item over time, while a weighted index number combines multiple items, each with a weight that reflects its relative importance. Weighted indices are more representative of overall changes because they account for the fact that some items matter more than others in a basket of goods.

How do I interpret an index number in an exam?

When interpreting an index number, always state the base year and explain the percentage change. For example, 'An index of 115 means the value is 15% higher than in the base year.' Avoid saying 'it increased by 115%' as this is incorrect. If it is a weighted index, mention that the change is a weighted average.

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