Define time series graph .

A time series graph is a line graph showing how a quantity changes over time. The measurements are plotted as points and joined in order with straight lines, drawn with a ruler.

What goes on each axis of a time series graph?

Time always goes on the horizontal axis. The quantity being measured or recorded goes on the vertical axis.

Why must the measurements for a time series graph be taken at regular intervals?

So that the points can be plotted at equal spacings along the time axis. Uneven spacing would distort the shape of the line and make the graph misleading.

When should the points on a time series graph be joined with dashed lines?

When the values in between the plotted points are unknown or meaningless. Ice creams sold on each day of the week is such a case, since there is no meaningful value halfway between Monday and Tuesday.

True or False? A time series graph and a vertical line graph are two names for the same thing.

False. A time series graph is a line graph, with its points joined up and time running along the horizontal axis. A vertical line graph shows the frequency of each of a set of discrete outcomes, and its lines are not joined at all.

What is a moving average, and what is it for?

A moving average is the mean of a number of successive observations, worked out again and again as the window slides along. It smooths out cyclical or seasonal ups and downs, which makes the underlying trend much easier to see.

How do you decide how many points a moving average should cover?

Enough points to cover one complete cycle, which usually means one whole year. That is why a four-point moving average is the commonest, for a year split into four quarters or four seasons.

Where is a four-point moving average plotted on a time series graph?

At the midpoint of the four time intervals it covers. So the average of the first four quarters is plotted halfway between the 2nd and the 3rd of them.

True or False? Moving average points should be joined up on a time series graph.

False. The moving average points are plotted but deliberately left unjoined. That is different from the raw data points on the same graph, which are joined up.

Which points is a trend line usually drawn through on a time series graph?

The moving average points, rather than the raw data points. That is more accurate, because the moving averages have already smoothed out the seasonal ups and downs.

True or False? A trend line is drawn by joining the moving average points to each other.

False. A trend line is a single straight line drawn approximately through the moving average points. Joining them point to point would just reproduce their wiggles instead of showing the overall direction.

A time series graph has no moving averages plotted on it. How can a trend line still be drawn by eye?

Draw it roughly halfway between the lowest and highest points of each cycle. That is less accurate than using moving averages, but it still shows the general direction of the data.

What is a seasonal trend, and how does it appear on a time series graph?

A pattern in the data that repeats itself over time, such as an ice cream shop selling more every summer and less every winter. It shows up as a repeating shape in the line, rising and falling the same way in each cycle.

Visitor numbers sit above the trend line in quarters 2 and 3 every year and below it in quarters 1 and 4. What does that show?

A seasonal variation, with more people visiting in spring and summer and fewer in autumn and winter. The weather and the school holidays are the obvious explanation, and a pattern like this repeats every year.

True or False? 'Mean seasonal variation' and 'average seasonal effect' mean the same thing.

True. They are two names for one quantity: the average amount by which a season's actual values differ from the trend line. A question may use either name, so both are worth recognising.

Why does a prediction made from a trend line get less reliable the further ahead it is made?

Because you are extending the trend line beyond the data it was drawn from. Trends and seasonal patterns can also change unexpectedly, so a prediction is most reliable only one cycle beyond the last known value.

GCSEStatisticsEdexcelHigherFlashcardsProcessing, Representing & Analysing DataTime Series

Time Series (Edexcel GCSE Statistics: Higher): Flashcards

Exam code: 1ST0

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FrontTime Series Graphs
Define time series graph.

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Cards in this collection (23)

Define time series graph.
A time series graph is a line graph showing how a quantity changes over time.
The measurements are plotted as points and joined in order with straight lines, drawn with a ruler.
What goes on each axis of a time series graph?
Time always goes on the horizontal axis.
The quantity being measured or recorded goes on the vertical axis.
Why must the measurements for a time series graph be taken at regular intervals?
So that the points can be plotted at equal spacings along the time axis.
Uneven spacing would distort the shape of the line and make the graph misleading.
When should the points on a time series graph be joined with dashed lines?
When the values in between the plotted points are unknown or meaningless.
Ice creams sold on each day of the week is such a case, since there is no meaningful value halfway between Monday and Tuesday.
True or False?
A time series graph and a vertical line graph are two names for the same thing.
False.
A time series graph is a line graph, with its points joined up and time running along the horizontal axis.
A vertical line graph shows the frequency of each of a set of discrete outcomes, and its lines are not joined at all.
What is a moving average, and what is it for?
A moving average is the mean of a number of successive observations, worked out again and again as the window slides along.
It smooths out cyclical or seasonal ups and downs, which makes the underlying trend much easier to see.
How do you decide how many points a moving average should cover?
Enough points to cover one complete cycle, which usually means one whole year.
That is why a four-point moving average is the commonest, for a year split into four quarters or four seasons.
Complete the formula for an $n$ point moving average.
$moving average = \frac{x_{1} + x_{2} + \dots +______}{______}$
The completed formula is:
$moving average = \frac{x_{1} + x_{2} + \dots + x_{n}}{n}$
Ten quarterly figures are given and you want four-point moving averages. How many will there be?
Seven.
Each average uses four consecutive figures and you stop when four are no longer left to make a full group, so ten points give $10 - 4 + 1 = 7$ averages.
The first four quarterly figures are 6.2, 8.5, 8.8 and 7.6. What is the first four-point moving average, and which figures does the second one use?
The first is $\frac{6.2 + 8.5 + 8.8 + 7.6}{4} = 7.775$ for those four quarters.
The second uses the 2nd to 5th figures, so each group overlaps the one before it by three values.
Where is a four-point moving average plotted on a time series graph?
At the midpoint of the four time intervals it covers.
So the average of the first four quarters is plotted halfway between the 2nd and the 3rd of them.
True or False?
Moving average points should be joined up on a time series graph.
False.
The moving average points are plotted but deliberately left unjoined.
That is different from the raw data points on the same graph, which are joined up.
Which points is a trend line usually drawn through on a time series graph?
The moving average points, rather than the raw data points.
That is more accurate, because the moving averages have already smoothed out the seasonal ups and downs.
True or False?
A trend line is drawn by joining the moving average points to each other.
False.
A trend line is a single straight line drawn approximately through the moving average points.
Joining them point to point would just reproduce their wiggles instead of showing the overall direction.
A time series graph has no moving averages plotted on it. How can a trend line still be drawn by eye?
Draw it roughly halfway between the lowest and highest points of each cycle.
That is less accurate than using moving averages, but it still shows the general direction of the data.
Complete the three descriptions of a general trend.
A trend line with a positive gradient shows a $______$ trend over time, one with a negative gradient shows a $______$ trend, and a horizontal one shows a $______$ trend.
The completed descriptions are:
A trend line with a positive gradient shows a rising trend over time, one with a negative gradient shows a falling trend, and a horizontal one shows a level trend.
What is a seasonal trend, and how does it appear on a time series graph?
A pattern in the data that repeats itself over time, such as an ice cream shop selling more every summer and less every winter.
It shows up as a repeating shape in the line, rising and falling the same way in each cycle.
Visitor numbers sit above the trend line in quarters 2 and 3 every year and below it in quarters 1 and 4. What does that show?
A seasonal variation, with more people visiting in spring and summer and fewer in autumn and winter.
The weather and the school holidays are the obvious explanation, and a pattern like this repeats every year.
Complete the formula for a seasonal variation at a point.
$seasonal variation =______- trend line value$
The completed formula is:
$seasonal variation = actual value - trend line value$
A point below the trend line therefore gives a negative seasonal variation.
True or False?
'Mean seasonal variation' and 'average seasonal effect' mean the same thing.
True.
They are two names for one quantity: the average amount by which a season's actual values differ from the trend line.
A question may use either name, so both are worth recognising.
Quarter 1 seasonal variations for three years are −1.34, −1.81 and −1.68. What is the mean seasonal variation for Quarter 1?
Add them and divide by three, keeping the minus signs: $\frac{- 1.34 - 1.81 - 1.68}{3} = - 1.61$ for that quarter.
A negative result means that quarter's values sit below the trend line on average.
The trend line gives 8.95 for Quarter 1 of 2024 and the average seasonal effect is −1.61. What is the predicted value?
Add the two together, giving $8.95 + (- 1.61) = 7.34$ thousand visitors.
A negative seasonal effect pulls the prediction below the trend line, which is what you would expect for a quiet quarter.
Why does a prediction made from a trend line get less reliable the further ahead it is made?
Because you are extending the trend line beyond the data it was drawn from.
Trends and seasonal patterns can also change unexpectedly, so a prediction is most reliable only one cycle beyond the last known value.

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