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 why is one used?

A moving average is the mean of a run of successive observations, worked out again and again as you move along the data. It smooths out the ups and downs of data that varies seasonally, which makes the underlying trend much easier to see.

For a four-point moving average, which data points does the second average use?

The 2nd, 3rd, 4th and 5th data points. Each group overlaps the one before it by three points, shifting along one place at a time, and you stop as soon as there are no longer four points left for a full group.

True or False? Ten data points give ten four-point moving averages.

False. The first group covers points 1 to 4 and the last covers points 7 to 10, so there are only seven groups altogether. You always run out at the end, because the last few points cannot make up a complete group of four.

On a time series graph with moving averages plotted, which points are joined up and which are not?

The raw data points are joined up in order with straight lines. The moving average points are left unjoined, which is easy to get wrong because the data points sitting beside them are joined.

What is a trend line, and why is one drawn on a time series graph?

A trend line is a single straight line drawn to show the general direction of the data over time. A time series can rise and fall so much that the overall pattern is hard to see, and the trend line answers whether things are broadly increasing, decreasing or staying level.

How is a trend line drawn when moving average points have been plotted?

As a line of best fit through the moving average points, drawn with a ruler. It is a single straight line passing approximately through them, rather than one that follows them exactly from point to point.

How can a trend line be drawn straight from a time series graph, without using moving averages?

By eye, running roughly halfway between the lowest and highest points of each cycle, which is usually each year. This is quicker but less accurate than using moving average points, which is why those are normally plotted first.

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

A seasonal or cyclical trend is a pattern in the data that repeats itself over time. It shows up as a repeating shape along the graph, such as an ice cream shop's sales rising every summer and falling again every winter.

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

A seasonal variation , with more people visiting in the spring and summer than in the autumn and winter. Comparing each point with the trend line, rather than with the point before it, is what separates the seasonal pattern from the general trend.

A graph of visitor numbers shows a rising trend. Why is 'there is a rising trend' not a complete answer on its own?

Because it describes the line rather than the situation the line is about. A complete answer adds what the line means for the quantity being measured, such as saying that the number of visitors is tending to increase over time.

True or False? A time series can show a rising general trend and still fall in some quarters.

True. The general trend describes the overall direction across a long period, while seasonal variation moves the individual values above and below it. Visitor numbers can drop every winter and still be rising year on year.

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Time Series (Edexcel GCSE Statistics: Foundation): Flashcards

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FrontTime Series Graphs
Define time series graph.

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Cards in this collection (19)

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 why is one used?
A moving average is the mean of a run of successive observations, worked out again and again as you move along the data.
It smooths out the ups and downs of data that varies seasonally, which makes the underlying trend much easier to see.
Complete the rule for choosing how many points a moving average covers.
The number of data points in each moving average must cover one complete $______$ , which in practice usually means one whole $______$ .
The completed rule is:
The number of data points in each moving average must cover one complete cycle, which in practice usually means one whole year.
That is why a four-point moving average is the commonest, since a year is often split into four quarters or four seasons.
For a four-point moving average, which data points does the second average use?
The 2nd, 3rd, 4th and 5th data points.
Each group overlaps the one before it by three points, shifting along one place at a time, and you stop as soon as there are no longer four points left for a full group.
Quarterly visitor numbers begin 6.2, 8.5, 8.8, 7.6 and 6.2 thousand. What are the first two four-point moving averages?
The first is the mean of the first four values, $\frac{6.2 + 8.5 + 8.8 + 7.6}{4} = 7.775$ thousand visitors.
The second shifts along one place, giving $\frac{8.5 + 8.8 + 7.6 + 6.2}{4} = 7.775$ thousand as well, which here happens to be the same.
True or False?
Ten data points give ten four-point moving averages.
False.
The first group covers points 1 to 4 and the last covers points 7 to 10, so there are only seven groups altogether.
You always run out at the end, because the last few points cannot make up a complete group of four.
On a time series graph with moving averages plotted, which points are joined up and which are not?
The raw data points are joined up in order with straight lines.
The moving average points are left unjoined, which is easy to get wrong because the data points sitting beside them are joined.
What is a trend line, and why is one drawn on a time series graph?
A trend line is a single straight line drawn to show the general direction of the data over time.
A time series can rise and fall so much that the overall pattern is hard to see, and the trend line answers whether things are broadly increasing, decreasing or staying level.
How is a trend line drawn when moving average points have been plotted?
As a line of best fit through the moving average points, drawn with a ruler.
It is a single straight line passing approximately through them, rather than one that follows them exactly from point to point.
How can a trend line be drawn straight from a time series graph, without using moving averages?
By eye, running roughly halfway between the lowest and highest points of each cycle, which is usually each year.
This is quicker but less accurate than using moving average points, which is why those are normally plotted first.
Complete the three kinds of general trend.
A trend line with a positive gradient shows a $______$ trend, one with a negative gradient shows a $______$ trend, and a horizontal one shows a level trend.
The completed kinds are:
A trend line with a positive gradient shows a rising trend, 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 show on a time series graph?
A seasonal or cyclical trend is a pattern in the data that repeats itself over time.
It shows up as a repeating shape along the graph, such as an ice cream shop's sales rising every summer and falling again every winter.
Visitor numbers sit above the trend line in quarters 2 and 3 of every year, and below it in quarters 1 and 4. What does that show?
A seasonal variation, with more people visiting in the spring and summer than in the autumn and winter.
Comparing each point with the trend line, rather than with the point before it, is what separates the seasonal pattern from the general trend.
A graph of visitor numbers shows a rising trend. Why is 'there is a rising trend' not a complete answer on its own?
Because it describes the line rather than the situation the line is about.
A complete answer adds what the line means for the quantity being measured, such as saying that the number of visitors is tending to increase over time.
True or False?
A time series can show a rising general trend and still fall in some quarters.
True.
The general trend describes the overall direction across a long period, while seasonal variation moves the individual values above and below it.
Visitor numbers can drop every winter and still be rising year on year.

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