Graphing

Scientists search for regularities and trends in data. To make it easier to find these regularities and trends, scientists often present data in either a table or a graph. Table belowpresents data about the pressure and volume of a sample of gas. You should note that all tables have a title and include the units of the measurements. The unit of pressure used here is atm (atmosphere).

You may note a regularity that appears in this table. As the pressure of the gas increases, its volume decreases. This regularity or trend becomes even more apparent when the data is graphed. A graph is a pictorial representation of the relationship between variables on a coordinate system.

When the data from Table above is plotted as a graph, the trend in the relationship between the pressure and volume of the gas sample becomes more apparent. The graph aids the scientist in the search for any regularity that exists in these data.

Drawing Line Graphs

Reading information from a line graph is easier and more accurate as the size of the graph increases. In the example above, the graph on the left uses only a small fraction of the space available on the graph paper. The graph on the right shows the same data but uses all the space available . If you were attempting to determine the pressure at a temperature of 110 K (Kelvin), using the graph on the left would give a less accurate result than using the graph on the right. When you draw a line graph, you should arrange the numbers on the axes to use as much of the graph paper as you can. If the lowest temperature in your data is 100 K and the highest temperature in your data is 160 K, you should arrange for 100 K to be on the extreme left of your graph and 160 K to be on the extreme right of your graph. The person who created the graph on the left did not take this advice and did not produce a very good graph. You should also make sure that the axes on your graph are labeled and that your graph has a title.

Reading Information from a Graph

When we draw a line graph from a set of data points, we are inferring a trend between known data points. This process is called interpolation. Even though we may only have a few data points, we assume that the line connecting these data points is a good model of what we're studying. Consider the following set of data for the solubility of KClO₃ in water.

Table below shows that there are exactly six measured data points. When the data is graphed, however, the person making the graph assumes that the trend between the temperature and the solubility remains the same. The line is drawn by interpolating the data points between the actual data points. Note that the line is not drawn by just connecting the data points in a connect-the-dot manner. Instead, the line is a smooth curve that reasonably connects the data points.

We can now reasonably read data from the graph for points that were not actually measured. If we wish to determine the solubility of KClO₃ at C, we follow the vertical grid line for C up to where it touches the graphed line and then follow the horizontal grid line to the axis to read the solubility. In this case, we would read the solubility to be 30. g/100 mL of H₂O at

C, C, and C, the graph would be the solid line shown in the graph below. If the solubility at

C was desired, we could extrapolate (the dotted line) from the graph and obtain a solubility of 5. g/100 mL of H₂O. If we check the more complete graph above, you can see that the solubility at

C is close to 10 g/100 mL of H₂O. The reason the second graph produces such a different answer is because the real behavior of potassium chlorate in water is more complicated than the behavior suggested by the extrapolated line. For this reason, extrapolation is only acceptable for graphs where there is evidence that the relationship shown in the graph will hold true beyond the ends of the graph. Extrapolation is more dangerous that interpolation in terms of producing possibly incorrect data.

In situations where it is unreasonable to interpolate or extrapolate data points from the measured data points, a line graph should not be used. Additionally, a line graph cannot be used for independent variables that reflect groups of discrete data, or non-numeric data. Frequently, a bar graph can be used instead. Consider the data in Table below.

For this set of data, you would not plot the data on a line graph because interpolating between years does not make sense. For example, you would not use this data to calculate the rainfall for the year 1980.5. Additionally, the amount of rainfall each year does not directly depend on the year. As a result, the bar graph shown below is better suited for this type of data.

From this bar graph, you could very quickly answer questions like, “Which year was most likely a drought year for Trout Creek?” and “Which year was Trout Creek most likely to have suffered from a flood?”

http://www.ck12.org/book/Introductory-Chemistry/r1/section/1.3/Introduction-to-Chemistry-and-The-Nature-of-Science-%253A%253Aof%253A%253A-Introductory-Chemistry/