Exploring distance time graphs

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# 3.3 Time-series graphs: summing up

So time-series graphs must be read with care. Adopt a questioning attitude when you are faced with a graph. Look carefully at the vertical axis to see just what the range of variation is, and at the horizontal axis to see what time intervals have been chosen. Ask yourself about the significance of this choice – what might be going on between each plotted point?

You might question whether the plotted variation is significant or whether it is the result of expected fluctuations. What about the accuracy of the figures, and the accuracy with which they have been plotted? Look at the line of the graph itself, if there is one. Points will not always be joined by straight lines – ask yourself what assumptions have been made about the progression from one time point to the next.

Now try the next activity. You are asked to perform a mathematical task in another example of an application of graphs. Tasks such as this are common choices for psychological experiments.

## Activity 3: Study patterns

In 1916, a study conducted on a class of psychology students at the University of California revealed a variation of study efficiency over the day. A group of 165 students were asked to give their preferred hours of study, and then undertook five repetitive memory tasks at one-hour intervals over three consecutive days. The tasks tested their ability to remember short sequences of numbers, to substitute numbers for symbols, to recognise geometrical figures, and to remember simple ideas.

A composite measure of efficiency was calculated for the group each hour. The results are given in Table 1. Column 1 gives the time of day, column 2 gives the corresponding relative efficiency measure, and column 3 lists the numbers of students preferring to study at that time of day.

Using your calculator, display the study efficiency data as a time-series graph. Which plotting window is appropriate to display this data?

Enter and display the study-time preference data as a time-series graph on your calculator.

What conclusions can you draw from these graphs about the study patterns of the students? Would your own study pattern fit into this picture? Note down your response.

### Discussion

Figure 6a shows the study efficiency data and Figure 6b shows the preferred study time, with each plotted against the time of day (using the 24-hour clock).

Students in the study preferred to work between 8 am and 10 am. The time-series graph shows that efficiency dropped markedly in the early afternoon. This dip also appears in other studies and seems to be independent of whether or not the subjects had a midday meal. The points on the graphs are connected by straight lines (they also could be connected by a smoothly curving line), indicating that no sudden changes are expected between the data points. From your own experience is this a reasonable assumption?

The graphs suggest that the preferred hours of work do not reflect the times of greatest ability (in terms of study efficiency), since the afternoon is unused. This may mean that students were unaware of the potential of the afternoons for studying, or simply that they preferred to do something else. What are your study patterns and preferences?

## Table 1 Preferred hours and study performance for the student group

Time of day Relative study efficiency Study time preference
08.00 100 110
09.00 104.2 150
10.00 106.7 90
11.00 105.5 40
12.00 no data no data
13.00 98.5 5
14.00 100.8 4
15.00 105 4
16.00 104 15
17.00 100.1 15
(Based on Palmer, J.D. (1976) An Introduction to Biological Rhythms, Academic Press, London, p. 142)

Here you have been reading about graphs; you were asked to consider ways of making interpretations from them and have used your calculator to display a graph. Look back to Activity 2 and note briefly which methods you feel are most useful in learning about graphs.

MU120_3

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