3 September 2008 MAR 110 HW4 -Graphs 1

Homework 4: Understanding Graphs

[based on the Chauffe & Jefferies (2007)] The term "datum" refers to one unit of information. The plural of datum is "data." In science data

typically consist of sets of numbers that are many times less easily understood in tables. A

pictorial representation of a set of numbers in a graph many times allows complex information

to be more easily understood in terms of changes, trends, and other relationships. There are many

types of graphs.

For example in a pie diagram (Figure 1-1), segments of a circle are used to represent

percentages of the whole. Bar diagrams (Figure 1-2) usually consist of sets of horizontal or

vertical bars in which the longer the bar, the larger the amount represented. A thermometer is a

very simple type of bar diagram in which the single bar- the height of the mercury - is represents

the temperature (the scale) at the moment.

The most commonly used graph in oceanography and other sciences is the line graph. It

typically consists of data that are plotted versus two variables that are represented on scales that

are perpendicular to each other. The horizontal scale is called the x-axis (or abscissa) and the

vertical scale is the y-axis (or ordinate). In the Figure 1-3 example, the two variables are (1) the

number of fish observed (the x-axis) at (2) different depths (the y-axis). The data from location A

3 September 2008 MAR 110 HW4 -Graphs 2

are connected by a line and compared with the data from location B. In general, the shape of the

lines reveals how the variables are related. In this case, the two lines indicate trends in the data,

which are in opposite directions. Specifically at location A, the number of fish observed

increased as the depth increased. The two variables have a direct relationship. The opposite

was true at location B, where the number of fish observed decreased as the depth increased -an

inverse relationship. Frequently, the relationships between variables can be much more

complex and the lines relating them are more irregular than the straight lines in this example.

A common graph displaying properties of the oceanography is called a profile graph, in which

the y-axis is depth and the x-axis is the variable measured versus depth, such as temperature,

oxygen content, salinity, pressure, velocity of sound, and/or water density. A variety of graphs

with different x-axis and y-axis scales are used. On some graphs, the scales are linear and the

distance between units is uniform (e.g., see Figure 1-5).

When comparing two graphs using the same units and scale type, be certain that the spacing

between units on the two graphs is identical. For example, if the units are 1 cm apart on one

graph but 2 cm apart on the other, the scales are not identical. Changing the spacing can

drastically alter the slope and shape of a line, making it appear steeper or gentler (Figure 1-4).

3 September 2008 MAR 110 HW4 -Graphs 3

Misinterpretation of the graphs will result if the difference in the scales in not recognized.

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EXERCISE -USING GRAPHS for DATA INTERPRETATION The data in the Table 1 were obtained by making measurements of ocean temperature using

eXpendable BathyThermograph (XBT) like the one depicted in Figure L1.1.

Figure L1.1 The expendable bathythermograph (XBT, right) is released from the launcher (left) by pulling the pin depicted to the right. The weighted devise falls through the water column spooling out thin copper wire that carries the temperature-related voltage up the wire to the ship where it is recorded.

Table 1. Ocean Temperature Profile Data

Depth

( m)

Temperature(oC)

Depth

( m)

Temperature

(oC)

Depth

( m)

Temperature

(oC)

0 32.00 11 26.00 40 3.20 1 31.00 12 24.25 50 3.00 2 30.50 13 20.50 60 2.90 3 30.25 14 19.50 100 2.70 4 30.00 15 17.00 200 2.60 5 29.75 16 14.20 300 2.50 6 29.40 17 11.30 400 2.40 7 29.15 18 09.00 700 2.30 8 29.03 19 07.00 800 2.20 9 29.00 20 05.75 900 2.10 10 28.50 30 03.40 1000 2.00

3 September 2008 MAR 110 HW4 -Graphs 5

Questions

1. Looking at the data in Table 1,

Answer the following questions:

a. What is the general relationship (direct or inverse) between temperature and depth?

b. Is this relationship consistent and uniform throughout? If not, explain how it varies.

c. What trends, if any, can be seen in data? 2. Plot the data on the linear graph in Figure 1-5. Answer the following questions regarding your plot. a. What is the general relationship (direct or inverse) between temperature and depth? b. Is this relationship consistent and uniform throughout the profile? c. What trends, if any, can be seen in data?

3. Was the tabular data set or the plot of the data on the graph more revealing easier to

understand? Why?