E13a — AQA GCSE Statistics

Test yourself on E13a with AQA GCSE practice questions.

7 days Premium · Then free forever · No card, no charge

Your focus

Know that sample size has an impact on reliability and replication.

E13a exam tips

Quick Revision Summary (Key Takeaway)

E13a in AQA GCSE Statistics covers the use and interpretation of index numbers, including weighted index numbers and the Retail Prices Index (RPI). Students must calculate index numbers, interpret changes over time, and understand how weighted indices reflect relative importance of items.

Topic Overview

Index numbers are a statistical tool used to compare changes in a variable over time, often expressed as a percentage relative to a base year. In AQA GCSE Statistics, E13a focuses on simple and weighted index numbers, including the Retail Prices Index (RPI), which measures inflation. Understanding index numbers is crucial for analysing economic data, comparing prices, and making informed decisions.

This topic builds on basic percentage change and ratio concepts. It is essential for interpreting real-world data such as inflation rates, wage growth, and cost of living adjustments. Mastery of index numbers also supports understanding of weighted averages and their applications in various fields, from economics to social sciences.

Key Concepts

→An index number expresses a value as a percentage of a base value, with the base year typically set to 100.
→Simple index number = (value in current year / value in base year) x 100.
→Weighted index numbers account for the relative importance of items by assigning weights; formula: sum of (index x weight) / sum of weights.
→The Retail Prices Index (RPI) is a weighted index used to measure inflation, based on a basket of goods and services.
→Index numbers allow comparison of changes over time and between different categories, but interpretation must consider the base year and weights.

Examiner Tips

💡Always show your working, especially the formula and substitution, to gain method marks even if the final answer is wrong.
💡When interpreting index numbers, relate them back to the context: state whether it is an increase or decrease and by what percentage.
💡For weighted index numbers, clearly identify the weights and show the sum of weights and sum of products to avoid arithmetic errors.

Common Mistakes

Students often forget to multiply by 100 when calculating index numbers, resulting in a decimal rather than a percentage. Correction: Always multiply by 100 to express as a percentage relative to the base.
Students may think that a higher index always means a higher value, but it depends on the base. Correction: Index numbers are relative; a value of 100 means no change from the base year.
When calculating weighted indices, students may simply average the indices without considering weights. Correction: Weighted indices require multiplying each index by its weight, summing, and dividing by the total weight.

Revision Plan

1Day 1-2: Revise the formula for simple index numbers and practice calculating them from given data. Ensure you can interpret results in context.
2Day 3-4: Learn the concept of weighting and practice calculating weighted index numbers. Focus on understanding why weights are used.
3Day 5-6: Study the Retail Prices Index (RPI) and its components. Practice interpreting RPI data and calculating inflation rates.
4Day 7-8: Complete past paper questions on index numbers, including both simple and weighted. Review mark schemes to understand common pitfalls.
5Day 9-10: Create a summary sheet of formulas and key interpretations. Test yourself with mixed problems and time yourself to build exam confidence.

Exam Question Types

📋Calculation of a simple index number given base and current values. Advice: Write the formula, substitute correctly, and multiply by 100.
📋Calculation of a weighted index number from a table of indices and weights. Advice: Show the sum of weights and sum of products clearly; double-check arithmetic.
📋Interpretation of an index number in context, such as explaining what a value of 115 means. Advice: State the percentage change relative to the base year.
📋Comparison of index numbers over time or between categories, often requiring a comment on inflation or price changes. Advice: Use specific figures and refer to the base year.

Command Word Expectations (AQA)

Calculate

In AQA GCSE Statistics, 'Calculate' requires you to work out a numerical answer using given data. You must show sufficient working to demonstrate the method, and give the answer with appropriate units or interpretation if asked.

Interpret

For 'Interpret', you must explain what the calculated index number means in the context of the problem. This typically involves stating whether there has been an increase or decrease and by what percentage relative to the base year.

Compare

When asked to 'Compare', you must identify similarities and differences between two or more sets of data or index numbers. Use numerical values and refer to the base year or weights to support your comparison.

How Students Lose Marks (Examiner Pitfalls)

Pitfall: Students often forget to multiply by 100 when calculating a simple index number, or they use the wrong base year. They may also confuse the base year with the current year.

❌ Weak Answer (Loses Marks):Index = (current value / base value) = 1.25, so the index is 1.25.

Example improved answer:Index number = (current value / base value) x 100 = (125 / 100) x 100 = 125. This means the value has increased by 25% since the base year.

Examiner Tip: Always write the formula, substitute the correct base and current values, and remember to multiply by 100. State clearly what the index number means in context.

Pitfall: When calculating a weighted index number, students may add the weights incorrectly or forget to divide by the sum of weights. They might also misinterpret what the weights represent.

❌ Weak Answer (Loses Marks):Weighted index = sum of (index x weight) = 2500, so the weighted index is 2500.

Example improved answer:Weighted index = sum of (index x weight) / sum of weights. For example, if weights are 2, 3, 5 and indices are 110, 120, 130, then weighted index = (110x2 + 120x3 + 130x5) / (2+3+5) = (220 + 360 + 650) / 10 = 1230 / 10 = 123. This means the overall weighted average has increased by 23% since the base year.

Examiner Tip: Clearly show the sum of weights and the sum of (index x weight). Double-check arithmetic. Interpret the result in the context of the problem.

Step-by-Step Worked Solutions

Question: The price of a loaf of bread was 80p in 2015 and 100p 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) = 80p and the current year value (2020) = 100p.
2.Step 2: Use the formula: Index number = (current value / base value) x 100.
3.Step 3: Substitute: (100 / 80) x 100 = 1.25 x 100 = 125.
4.Step 4: Interpret: An index of 125 means the price in 2020 is 125% of the price in 2015, i.e., a 25% increase.

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

Question: A weighted index number is calculated for a basket of goods with three items: Item A (weight 3, index 110), Item B (weight 5, index 120), Item C (weight 2, index 150). Calculate the weighted index number and explain what it represents.

1.Step 1: Multiply each index by its weight: A: 110 x 3 = 330, B: 120 x 5 = 600, C: 150 x 2 = 300.
2.Step 2: Sum these products: 330 + 600 + 300 = 1230.
3.Step 3: Sum the weights: 3 + 5 + 2 = 10.
4.Step 4: Divide the sum of products by the sum of weights: 1230 / 10 = 123.
5.Step 5: Interpret: The weighted index is 123, meaning the overall weighted average of the basket has increased by 23% since the base year.

Final Answer: Weighted index number = 123. This indicates a 23% increase in the weighted average of the basket of goods.

Active Recall Memory Test

What is the formula for a simple index number?

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

How do you calculate a weighted index number?

Key Fact: Weighted index = sum of (index x weight) / sum of weights.

What does an index number of 100 signify?

Key Fact: An index of 100 means the value is unchanged from the base year.

What is the Retail Prices Index (RPI) used for?

Key Fact: RPI is a weighted index used to measure inflation by tracking the price changes of a basket of goods and services.

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 typically set to 100. It allows comparison of values across different time periods, such as prices or quantities. For example, if the price of an item increases from £10 to £12, the index number is 120, indicating a 20% increase from the base year.

How do I calculate a weighted index number?

To calculate a weighted index number, multiply each item's index by its weight, sum these products, and then divide by the sum of the weights. This gives a weighted average that reflects the relative importance of each item. For instance, if item A has index 110 and weight 2, and item B has index 120 and weight 3, the weighted index is (110x2 + 120x3) / (2+3) = (220+360)/5 = 116.

What is the difference between simple and weighted index numbers?

A simple index number compares a single item's value to its base value, while a weighted index number combines multiple items, each with a weight reflecting its importance. Weighted indices are more representative of overall changes because they account for the relative significance of different components. For example, the RPI is a weighted index that reflects the average price change of a basket of goods.

Why is the base year important in index numbers?

The base year serves as the reference point for all comparisons, with its index set to 100. It allows consistent measurement of changes over time. Choosing an appropriate base year is crucial because it can affect the interpretation of trends; a base year with unusual values might distort the index. In exams, the base year is usually given, and you must use it correctly in calculations.

How do I interpret an index number like 115?

An index number of 115 means the value has increased by 15% compared to the base year. It indicates that the current value is 115% of the base value. For example, if the base price was £200, the current price would be £230. Always relate the index to the context to explain what the change means, such as a price rise or increase in output.

What common mistakes should I avoid in index number questions?

Common mistakes include forgetting to multiply by 100, using the wrong base year, and ignoring weights in weighted indices. Also, students often misinterpret the index by not stating the percentage change. To avoid these, always write the formula, double-check the base and current values, and clearly interpret your result in the context of the question.

Your focus

E13a exam tips

More AQA GCSE Statistics topics

Cookies on MasteryMind