GCSE Time series Practice Questions

Find the time on the horizontal axis

The times run along the bottom of the graph in order. Find Q3 2022 on that axis before reading anything off.

Go straight up to the plotted point

Move up from Q3 2022 until you meet the point on the line. That point is the reading for that time.

Read across to the vertical scale and state the reading

Going across from that point to the vertical scale gives $50$, so umbrellas sold in Q3 2022 was $50$.

Look at the steepness of each step, not the height of the points

The greatest increase is about how far the line moves between two points next to each other, not about which point is highest.

Work out the change at every step

Take each reading away from the one after it. The signs show which way the line moved.

State the answer

So the greatest increase is: Between Week 1 and Week 2.

Look at the steepness of each step, not the height of the points

The greatest fall is about how far the line moves between two points next to each other, not about which point is highest.

Work out the change at every step

Take each reading away from the one after it. The signs show which way the line moved.

Pick out the biggest fall

The biggest fall on the whole graph is $16$.

Find where it happens

That change takes the reading from $60$ in Q1 2023 to $44$ in Q2 2023.

Check the runners-up

The next biggest changes are all smaller than $16$, so there is no tie.

State the answer

So the greatest fall is: Between Q1 2023 and Q2 2023.

Split the readings up year by year

A seasonal pattern is about what happens INSIDE each year, so take one year at a time.

Find the lowest reading in each year

In each year the lowest point of the line comes in Quarter 2.

Check that quarter is the same every year

Every year has its lowest reading in Quarter 2, so the pattern repeats — that is what "seasonal" means.

Check Quarter 1 is not the lowest

In 2022, Quarter 1 reads $56$ while Quarter 2 reads $28$, so Quarter 1 is not the lowest.

Check the other quarters as well

Written out in full, the 2022 readings show Quarter 2 clearly below the rest.

Rule out "it is different every year"

The lowest quarter is Quarter 2 in every year, so the option saying it varies is wrong.

Notice the lowest readings themselves change

The Quarter 2 readings are not identical from year to year — a seasonal pattern is about the shape of the line, not about identical numbers.

Say what a seasonal pattern is

A seasonal pattern means the same rise and fall happens at the same time each year — like coats selling every winter.

Keep the season and the trend apart

The seasonal pattern says WHEN the peaks and dips come; the trend says whether the whole line is drifting up or down. They are different questions.

State the answer

So the correct statement is: The lowest reading comes in Quarter 2 of every year.

Look at the whole line, not one step of it

A trend is the general direction of travel once the ups and downs are ignored. It is never decided by a single pair of points.

Work out the change from each point to the next

Some of these are positive and some are negative, so the line goes up and down. Those swings are the seasonal pattern, not the trend.

Compare the first half of the period with the second half

The first $6$ readings total $380$ and the last $6$ total $316$. Comparing equal-sized blocks like this cancels out the seasonal swing.

Draw a trend line through the points

One straight line drawn through the middle of the points shows the overall direction at a glance.

Look at the gradient of that trend line

The trend line falls from left to right, so its gradient is negative.

Say what that gradient means

A negative gradient means the readings decrease over the period as a whole.

Rule out "it increases every single time"

The line falls from Q1 2022 to Q2 2022, so it is simply not true that the readings rise every time.

Rule out "it decreases every single time"

The line rises from Q2 2022 to Q3 2022, so it does not fall every time either.

Rule out the opposite trend

The second half of the period is clearly lower than the first, so a upward trend is impossible.

Rule out "no trend"

The two halves differ by $-64$, which is far too big to call the readings "about the same".

Keep the season and the trend apart

A time series can have a strong seasonal pattern AND a clear trend at the same time. Describing one does not describe the other.

Compare the same point one cycle apart

Comparing like with like — the same quarter a year apart, say — is another way to see the trend without the season getting in the way.

Say how far a trend can be trusted

The trend describes what happened over the period on the graph. Carrying it far into the future is guesswork, not mathematics.

Put the description into words

Overall the readings decrease over time, with a seasonal rise and fall on top of that.

State the answer

So the correct description is: There is a downward trend: overall the readings decrease over time.