Using The Central Point
Making Comparisons
Curve v Line
Checking Trend Lines
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Improving your Line
It is not easy to draw a (trend) line showing the pattern. The
points seldom lie exactly on any one line. We try to draw a
straight line which goes close to most points and shows the
general direction. One point we make certain lies on the line is
the central point.
Using the Central Point
| Year |
Number of
attendances
(millions) |
Average admission
prices
(to nearest 1p) |
| 1965 |
327 |
19 |
| 1966 |
289 |
21 |
| 1967 |
265 |
22 |
| 1968 |
237 |
25 |
| 1969 |
215 |
27 |
| 1970 |
193 |
31 |
| 1971 |
176 |
34 |
| 1972 |
157 |
38 |
| 1973 |
134 |
43 |
| 1974 |
138 |
50 |
| 1975 |
116 |
62 |
(Source: Annual Abstracts)
Table 3 - Cinema attendances and average admission prices,
1965-1974.
- Draw a horizontal axis with a scale from 1965 to 1977 and
a vertical axis from 0 to 350 millions.
- Plot the attendance numbers on the graph, marking each
point with a +.
- Find the mean number of attendances over the period
1965-1975. (Add up all the attendances and divide by 11.)
The middle of the time period lies on the line through 1970.
- Plot the mean number of attendances on this halfway line.
This is called the CENTRAL POINT.
- Why should the line pass through this point?
- Now use a transparent ruler and draw in your trend line,
making sure it passes through the central point and is as
close to the other points as possible.
Some of the points will lie above the line and some below.
- Use your fine to predict the attendances for 1976 and
1977.
- *Compare your predictions with those of your neighbours.
If they are very different, compare your trend lines.
Tracing paper may help if you have used the same scales.
The actual values were:
1976 - 104 millions
1977 - 103 millions
- Find the errors in your estimates.
Making Comparisons
- Plot the average prices given in Table 3 against time in
years, on a graph.
- Work out the mean admission charge and plot the central
point.
- Draw in the trend line, making sure it passes through the
central point.
- Extend the line and use it to predict average admission
charges for 1976 and 1977.
- Look at the trend line you drew for cinema attendance and
compare it with this one. Try to draw some conclusions
about the future of cinema attendances, and make a list
of possible outcomes.
The actual figures for cinema admission prices were: 1976 -
73p 1977 - 83p
- Does this new information affect your answer to e? Try to
answer e again, using this new information.
Curve v Line
Look again at the points you plotted for average prices.
- Do you think the points look as though they should lie on
a straight fine?
Try to draw a curve which fits the data more closely.
- Use your curve to estimate the admission charges for 1976
and 1977. Compare these answers with the ones you
obtained from the straight line, and write down what you
notice.
- Which gave the better estimates - the straight line or
the curve? Explain your answer.
Checking Trend Lines
Look back at the lines vou drew in Section B2.
- Work out the position of the central point for those
data, and plot it on your graph.
- Does your line pass through that point? If not, draw a
trend line through the central point and use this line to
give new estimates of the figures for 1975, 1977 and
1985.
- Compare these estimates with your previous ones. Which
are nearer the actual figures?
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