# GCSE Statistics Chapter 6 Summary- Time Series

After completing this chapter, you will be able to;

• Draw line graphs
• Plot points as a time series on a graph
• Draw a trend line by eye
• Use a trend line to make a prediction
• Calculate and plot appropriate moving averages
• Identify seasonal variations by eye
• Work out mean seasonal variations
• Draw a trend line based on moving averages
• Recognise seasonal effects at a given point and mean seasonal effect
• Interpret time series graphs
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Line graphs
1.) A line graph is used to display data when the two variables are not related
by an equation and it is uncertain what happens between the plotted points.
2.) A time series is a set of observations taken over a period of time. A line
graph can be used to show a time series. When plotting a time series, time is
plotted on the horizontal axis.
Trend Lines
3.) A general trend is the way that the data change over time.
4.) A trend line shows the general trend of the data.
5.) A trend line may show a tendency to rise, to fall or to stay level.
6.) Variations in a time series may be
A general trend (as shown by the trend line)
Seasonal variations (a pattern that repeats)
Moving averages
7.) A moving average is an average worked out for a given number of
successive observations.
8.) The number of point in each moving average should cover one complete
cycle of seasons.
9.) Moving averages are plotted on the time series graph to help show the trend.
10.) They are plotted at the midpoint of the time intervals they cover.
11.) The points plotted for moving averages should not be joined up.
Estimating seasonal variations and making predictions
11.) Seasonal variation at point= actual value ­ trend value
12.) Estimated mean seasonal variation for any season = mean of all the
seasonal variations for that season
13.) Predicted value = trend line value + estimated mean seasonal
variation
Calculating the equation of a trend line

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The equation of a trend line is y = ax + b where a is the gradient of the
trend line and b is the intercept with the yaxis.
15.) The constant a is the amount by which the trend increases per time period
(quarter, twomonths, etc.)
16.) The constant b is the value of the trend at the end of the last period before