Problem solving with scatter graphs and time series | Maths

Starter quiz

______ is when you estimate values that are within the range of available data.

'Interpolation' ✓
This time series graph shows the temperatures in Sheffield between 2012 and 2019. In how many quarters does the mean maximum temperature reach between 10°C and 20°C? ______ quarters.

'17' ✓
This scatter graph shows ______ correlation.

'positive' ✓
The time series below shows data from the ONS about the average annual income per person each year. What is the approximate median income in the year 2014?

£20 000

£25 000

£30 000 ✓

£35 000
The time series below shows data from the ONS about the average annual income per person each year. What is the approximate smallest difference between the mean and median incomes?

£1000

£3000 ✓

£5000

£10 000
The time series graph shows data on average houses prices over a number of years in the UK. The graph shows ______ years where average house prices were below £200 000

'11' ✓

Exit quiz

Lucas plots this scatter graph. He says, “Point P must be an error.” Is Lucas definitely correct?

Yes, the point does not fit the rest of the data.

No, it is just an unusual result.

It depends, outliers should be investigated further. ✓
This scatter graph shows positive correlation. Which of these Oak pupils are correct?

Aisha: Both variables might be affected by a third variable. ✓

Jacob: one variable is definitely causing the other to increase.

Lucas: The variables might be completely unrelated and correlate by chance. ✓

Laura: One variable might be causing the other to increase. ✓
______ is when you estimate values that are outside the range of available data.

'Extrapolation' ✓
The time series graph shows data about the number of daily internet users in England. Sam says, “I can use the graph to predict there will be 90 million internet users in Wales in 2050.” Is Sam right?

Yes, you can continue the trend for another 10 years.

Yes, there is a clear upward trend which is likely to continue.

No, you cannot use data for England to predict for Wales. ✓

No, there is unlikely to be 90 million people in Wales in 2050
A scatter graph is a visual representation for ______ data.

'bivariate' ✓
A reporter writes the following headline for the Oak Daily News. Which of these Oak pupils are correct?

Andeep: Wow! That cannot just be coincidence.

Jun: The two variables have a negative correlation so the headline is true.

Lucas: Hannah's a popular name at the moment, it is unrelated to landlines. ✓

Sam: There must be a third factor at play to link these.

Worksheet

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Video

Lesson Details

Key learning points

Errors in drawing the graph will produce incorrect conclusions
Outliers may just be unusual results
These types of graphs are widely used in the media and can be misinterpreted

Common misconception

A plausible conclusion or claim must be true when it is presented with data.

Graphs can be misinterpreted, which can lead to invalid conclusions.

Keywords

Time series graphs - Time series graphs show data over a time period. The time period is always shown on the x-axis. Data points are joined chronologically by line segments.
A scatter graph - A scatter graph is a visual representation for bivariate data. It can be useful when determining the nature of the relationship between the variables.