Index Numbers & Rates of Change (Edexcel GCSE Statistics: Higher)

The table gives the chain base index numbers for the average monthly rent for apartments in a city in January for each of the years 2016 to 2019.

Describe what the chain base index numbers show about the average monthly rent for apartments in January for the years 2016 to 2019.

In January 2017, the average monthly rent for apartments in the city was £1 200.

Calculate the average monthly rent for apartments in January 2016.
Give your answer correct to the nearest £.

Sarah is analysing the average price per kilogram of fresh fruits sold in a local market over five consecutive years during the spring season.

The table gives the average price per kilogram, in pounds (£), for fresh fruits over the years. It also provides two of the chain base index numbers, correct to one decimal place, for this information.

Find the chain base index numbers for 2018 and 2019 and write them in the table.
Give each value correct to one decimal place.

(i) Find the geometric mean of the four chain base index numbers.

You must show your working.

Give your answer correct to one decimal place.

[2]

(ii) Interpret your answer.

[2]

The table below gives the price index number for the average cost of household electricity in a particular country for each of six years, with 2015 as the base year.

The table also provides some of the chain base index numbers for the same information.

Find, correct to 2 decimal places, the chain base index number for 2020.

A student studying the data wanted to find the percentage increase in the cost of household electricity between 2018 and 2019.

Here is the student's working:

Explain whether or not the student is correct.

The geometric mean of the chain base index numbers for 2016 to 2019 is 102.30.

Interpret this geometric mean in the context of the average cost of household electricity.

Using July 2015 as the base month, the table shows some of the index numbers for the consumer price index (CPI) from July 2015 to July 2023.

Source: www.ons.gov.uk

Give an interpretation of the index number 107.9 in the table.

The CPI is a weighted index. It measures the changes in the prices of consumer goods and services. All items are classed as either goods or services.

The table below shows the weightings used for CPI in 2024.

Source: www.ons.gov.uk

In July 2024, the index for services was 137.8

Using this information and the table in part (a), calculate the index number for goods in July 2024.

Give your answer to the nearest whole number.

One of the items included in the services index is the price of hairdressers.

Assess whether or not it is appropriate to use 137.8 in order to find an estimate of the change in the price of hairdressers from July 2015 to July 2024.

The table gives the populations, in thousands, and the crude birth rates for two regions of a particular country in 2024.

The table also gives the total population, in thousands, of the same country in 2024.

In 2024 the number of births in the country was 792 814.

Using the formula above, work out the crude birth rate for the country in 2024.

Give your answer correct to one decimal place and write your answer in the table.

Work out the number of births in region A in 2024.

Terry says that without doing any calculations he knows there were fewer births in region B than in region A in 2024.

Using the information in the table, explain why Terry is correct.

Changes in the cost of living in the United Kingdom are measured by the consumer price index (CPI).

The table shows the index numbers for August 2023, using 2015 as the base year, of the food items that contribute to the Consumer Prices Index (CPI) for food.

The table also shows the weightings for how the spending by the Smith family is divided between these items.

Source: Office for National Statistics

Using 2015 as the base year, the overall CPI figure for food for August 2023 was 133.7.

Compare the overall change in the cost of food for the Smith family between 2015 and August 2023 with the change in the CPI for food between 2015 and August 2023.

Explain whether or not it is possible to conclude from your calculations that the Smith family is financially better off or worse off in August 2023 as compared with 2015.

The table shows the value of the gross domestic product (£ million) of the UK for each quarter from 2021 quarter 4 to 2024 quarter 2.

Source: Office for National Statistics, GDP Data Tables

According to the table, between which two consecutive quarters was there the lowest increase in GDP?

Using 2021 Quarter 4 as the base, work out the simple index number for the gross domestic product of the UK in 2024 Quarter 1.

Give your answer correct to the nearest whole number.

The gross domestic product simple index number for 2024 Q3 is 118.71 when 2021 Q4 is used as the base.

Calculate the value of the gross domestic product, in millions of pounds, of the UK in 2024 Q3 to the nearest whole number.

If 2021 Q4 is used as the base, describe what is happening to GDP, relative to 2021 Q4, for a year with the following GDP simple index numbers.

The table gives the crude birth rates and crude death rates, per 1000 people, for two South American countries in the year 2022.

Source: www.data.worldbank.org

Anna concludes that the crude birth rate and the crude death rate for Uruguay shows that the population of Uruguay increased in 2022.

Explain how the data can be used to support Anna's conclusion.

Give a reason why the data might not support Anna's conclusion.

In 2022 the total population of Paraguay was 6 780 744.

Using the formula below, work out the number of births in Paraguay in 2022.

The standard population of Paraguay and of Uruguay for three different age groups in 2022 is shown in the table.

Source: www.data.worldbank.org

Give an interpretation of the number 289 in the table.

Compare the crude death rate for Paraguay with the crude death rate for Uruguay.

By referring to the information in the Standard population table, suggest a reason for your comparison.