Time series and moving averages

The time series graph gives information about the revenue, in $ billion, for the skiing resort of Vail each quarter from Quarter 1, 2018 to Quarter 1, 2023

For which year and quarter was the revenue the greatest?

The 4‑point moving averages for the data and the trend line are also plotted on the grid.

Explain why it is appropriate to calculate 4‑point moving averages for this set of data.

Describe and interpret the trend shown by the time series graph.

Compare and interpret the seasonal variation for each quarter of the revenue for the years 2018 to 2022

A council wants to encourage people to use the council leisure centres. The council has put advertisements in the town centres to tell people about the opening times and the available facilities in the leisure centres.

Nico has been asked to find out if the advertising has been successful. He plans to use cluster sampling where the clusters are customers at each leisure centre. For the selected clusters he will ask the customers to complete a questionnaire about the advertisements.

Comment on the suitability of Nico’s plan for sampling in this context.

Keti suggests that they should do a pilot study before they give out the questionnaire.

Give a reason why it is appropriate to do a pilot study.

The council also gave a voucher for one free admission to every child in the county.

The council thinks that some people have collected and used more than one of the free admission vouchers per child. Nico is going to include a question about this on the questionnaire. He thinks that he should use the random response technique.

Explain why it is appropriate to use the random response technique in this context.

Design a random response question that Nico could use on the questionnaire in order to collect this information.

Nico wants to find out if the number of people using the leisure centres increased after the advertisements and vouchers started a month ago.

He would also like to predict the number of people likely to use the leisure centres in the future.

Here is the plan for his investigation.

Discuss whether Nico’s plans for collecting, processing and presenting data are appropriate.

Divyesh is investigating the number of games won by two Los Angeles basketball teams, the Clippers and the Lakers. He collects some data from the NBA website.

Complete the sentence with an appropriate statistical word.

Divyesh has collected data from the internet and so this is_........ data.

Using the information in the bar chart to compare the number of games won by each team over the four years,

write down one comparison between the two teams,

describe the trend in the number of games won by the Lakers over the four seasons.

The table contains information about the number of games won by the Clippers in the 2022–23 season.

Complete the table. Give your answers correct to the nearest whole number.

The line graph shows the cumulative games played and the cumulative percentage of games won by the Lakers in the same season.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Each team played 82 games in the 2022–23 season.

Which team won the most games by the end of the 2022–23 season? You should justify your answer.

Divyesh is investigating the number of games won by two Los Angeles basketball teams, the Clippers and the Lakers. He collects some data from the NBA website.

Complete the sentence with an appropriate statistical word.

Divyesh has collected data from the internet and so this is_........ data.

Using the information in the bar chart to compare the number of games won by each team over the four years,

write down one comparison between the two teams,

describe the trend in the number of games won by the Lakers over the four seasons.

The table contains information about the number of games won by the Clippers in the 2022–23 season.

Complete the table. Give your answers correct to the nearest whole number.

The line graph shows the cumulative games played and the cumulative percentage of games won by the Lakers in the same season.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Each team played 82 games in the 2022–23 season.

Which team won the most games by the end of the 2022–23 season? You should justify your answer.

Describe and interpret the trend shown by the graph.

Discuss any seasonal variation shown by the graph and interpret one in context. Do not do any calculations.

Work out the mean seasonal variation for Quarter 1 Give your answer correct to 1 decimal place.

Interpret your answer to part (c)(i) in context.

Use your answer to part (c)(i) and the time series graph to predict the number of visitors to Canada from the UK in Quarter 1 of 2020 You must show your working.

Discuss the reliability of using your answer to part (c)(i) to predict the number of visitors to Canada from the UK in Quarter 1 of 2025 Give a reason for your answer.

Claire is investigating sales of different types of vehicle over time. She plans to collect data on the numbers of motorcycles first registered in the UK over time.

Write down a suitable hypothesis for this investigation.

The time series graph shows some information about the numbers of motorcycles first registered in the UK from 2017 to 2019

Identify and interpret one example of seasonal trend shown by the time series graph.

Claire calculated 4-point moving averages for the information shown in the time series graph.

Explain why this is appropriate.

Claire also collected data on the numbers of cars first registered in the UK from 2017 to 2019

The time series graph shows some information about the numbers of cars first registered in the UK from 2017 to 2019 together with the first seven 4-point moving averages.

Compare the seasonal trend shown for the numbers of motorcycles first registered in the UK with the seasonal trend for the numbers of cars first registered in the UK.

The last three 4-point moving averages (thousands) for the number of cars registered in the UK from 2017 to 2019 are 576.0 575.3 573.9

Plot these three moving averages on the time series graph and draw a trend line.

Describe and interpret the trend in the numbers of cars first registered in the UK from 2017 to 2019

The table gives information about the numbers, in thousands, of overseas visitors to the United Kingdom from North America.

(Source: Office for National Statistics)

The table also gives the 4-point moving averages for the data in the table.

Explain why it is appropriate to calculate 4-point moving averages for the data in the table.

The time series graph has been plotted on the grid below for the data in the table.

Twelve of the 4-point moving averages for the data in the table have also been plotted on the grid so that the final 4-point moving average is missing from the grid.

Plot this 4-point moving average on the grid.

1	2	3	4	1	2	3	4	1	2	3	4	1	2	3	4
	2015	2016	2017	2018

Draw a trend line for the time series graph.

Jo wants to predict the number of visitors to the United Kingdom from North America for the first quarter of 2019

She is going to use the time series graph, the trend line and an average seasonal effect.

Describe how Jo should use these to obtain her prediction.

The time series graphs show information about the numbers of births recorded in England and Wales for girls named Chloe and for girls named Evelyn in the years 2000 to 2017

(Source: Office for National Statistics)

For the year 2017, write down the number of births recorded for girls named Evelyn.

For the year 2017, there were more births recorded for girls named Evelyn than for girls named Chloe.

How many more?

For the years 2000 to 2017, describe the trend for

girls named Chloe,

girls named Evelyn.

The time series graph shows information about the annual inflation rate in the UK each

Quarter and Year (Source: ONS

Describe and interpret the trend in the annual inflation rate from 2015 to 2017

The table gives the annual inflation rate for the first two quarters of 2018

Plot this information on the time series graph.

Show that the first 4-point moving average for the data values in the time series graph is 0.375

Alex wants to use the time series graph to describe the changes in the annual inflation rates.

He subtracts the annual inflation rate of the first data point from the annual inflation rate of the last data point on the time series graph.

Explain whether or not this is an appropriate method for Alex to use.

Describe the trend in visitor numbers to the museum over these three years.

For which quarter each year does the museum have the fewest visitors?

David has drawn a right-angled triangle on the graph from 2015 Quarter 1 to 2016 Quarter 4 so that he can calculate the gradient of the trend line, correct to one decimal place.

Here is his calculation.

Interpret, in context, the gradient of 1.4

David used the trend line and mean seasonal variation (or average seasonal effect) to predict the number of visitors to the museum for Quarter 2 of 2018

Comment on the validity of a prediction found in this way.

The actual number of visitors to the museum in Quarter 2 of 2018 was 203 100

Determine how close David’s prediction was to 203 100