Time Series (Edexcel GCSE Statistics: Higher)

The table below gives information about the number of visitors to a website, in thousands.

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

The time series below shows all the data points from the table in part (a), as well as the first twelve 4-point moving averages.

The final 4-point moving average is missing from the grid.

Calculate the value of the final 4-point moving average and plot it on the grid.

Draw a trend line for the time series graph.

The owner of the website wants to predict the number of visitors to the website for the first quarter of 2024.

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

Describe how they should use these to obtain a prediction.

The number of downloads of a gaming app is shown on the time series graph below.

It shows information about the quarterly number of downloads for 2020 to 2023, with the number of quarterly downloads shown in thousands.

Between which two quarters each year from 2020 to 2023 was the increase in app downloads the highest?

Describe the seasonal trend shown by the time series graph.

An analyst working for the company who produces the gaming app uses –point moving averages for the information shown in the time series graph in order to help determine the trend.

Write down an appropriate value of . Give a reason for your answer.

The analyst uses the time series graph to predict the number of app downloads for 2024 Quarter 3.

Discuss the reliability of the analyst’s prediction.

The table and time series graph give information about the number of visitors, in thousands, to a National Park each quarter from Quarter 1, 2018, to Quarter 3, 2020.

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

The eighth 4-point moving average for the data is 1475. Plot this moving average on the grid.

Draw a trend line for the time series graph.

The average seasonal effect for Quarter 4 is found to be −120 thousand.

(i) Give an interpretation of this value.

[1]

(ii) Calculate an estimate of the number of visitors to the National Park in Quarter 4, 2020.

[2]

Write down two assumptions that have to be made so that your estimate in part (d)(ii) is valid.

The time series graph shows information about the quarterly sales of electric vehicles (EVs) in a country, in thousands, from 2018 Quarter 1 to 2020 Quarter 4.

Identify one example of the seasonality shown by the time series graph.

A researcher calculated the 4-point moving averages for the data.

Here are their results.

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

Describe the trend shown in the graph in context.

The researcher estimates that the sales of EVs in 2021, Quarter 2 will be approximately 68 thousand vehicles.

The average seasonal effect for Quarter 2 is found to be +2.18 thousand across the three years shown.

Use the average seasonal effect for Quarter 2 to comment on the researcher’s estimate.

Explain why calculating 4-month moving averages is appropriate for this data.

The table below shows the number of cars sold by a car dealership each week, over several months, starting in February.

The manager of the car dealership calculates the 4-point moving average for each month.

Calculate the third 4-point moving average for the data shown.

The time series graph below shows the data from the table. All 4-point moving averages have been plotted except the third one.

(i) Use your calculated value from part (a) to plot the third 4-point moving average on the graph.

[1]

(ii) Draw a trend line for the time series graph.

[1]

Describe the trend, in context, for the number of cars sold in the period shown.

Calculate an estimate of the mean seasonal variation for week 4 across the five months shown.

The time series graph and the trend line show information about the value of sales, in thousands of pounds per quarter, for a new business during the years 2019, 2020, and 2021.

Describe the trend in sales for the business over these three years.

For which quarter, each year, does the business have the lowest value of sales?

Marie has drawn a right-angled triangle on the graph from 2019, Quarter 1 to 2020, Quarter 4 so that she can calculate the gradient of the trend line, correct to one decimal place.

Here is her calculation

Interpret, in context, the gradient of 9.3

Marie extended the trend line further and used the trend line and the mean seasonal variation (or average seasonal effect) to predict the value of sales for Quarter 1 of 2022.

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

The graph with the extended trend line that Marie used is shown below.

The actual value of sales in Quarter 1 of 2022 was £264 000.

Determine how close Marie's prediction was to £264 000.

The impact of a new roundabout being built at a junction is being investigated.

The table below shows the number of vehicles passing a primary school nearby over 28 days.

The first 7 days show vehicle counts before a new roundabout was installed at the end of Day 7. The following 21 days show counts after the roundabout has been implemented.

Calculate the fourth 7-point moving average for the data.

One of the targets of the new roundabout is to decrease the number of vehicles passing the primary school.

The 7-point moving averages for data in the table are used to create a trend line.

The equation of the trend line is

Does this trend line suggest that the target has been met? Give a reason for your answer.

Suggest why 7-point moving averages have been used for this investigation.

The table below shows the number of sales for a small online business each quarter for 4 years.

Explain why it is appropriate to calculate the 4-point moving average for this data.

The time series graph below shows the data from the table above, and most of the 4-point moving averages.

Two of the 4-point moving averages are missing.

(i) Calculate the two missing 4-point moving averages.

[2]

(ii) Use the moving averages to draw a trend line on the graph.

[2]

Use the data in the table, and the trend line drawn on the graph in part (b), to calculate the mean seasonal variation for Quarter 3.