AP* Environmental Science Grappling with Graphics & Data

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1 Part I: Data, Data Tables, & Graphs AP* Environmental Science Grappling with Graphics & Data You will be asked construct data sets and graphs from data sets as well as to interpret graphs. The most common analyses involve interpolating data within a data set or extrapolating data beyond a data set. When you are analyzing data, contemplate the independent vs. dependent variables. The independent variable is the one the experimenter is controlling; it may help to think of it as the input. It may also help to embrace this simple graphic to help you remember what goes where as you design your graph. DRY is an acronym for Dependent or Responding variable is plotted on the y-axis. while MIX is an acronym for Manipulated or Independent variable is plotted on the x-axis. Shall we practice? DRY MIX Example 1 If a scientist conducts an experiment to test the theory that a vitamin could extend a person s lifeexpectancy, then the independent variable is the amount of vitamin that is given to the subjects within the experiment. This is controlled by the experimenting scientist. The dependent variable, or the variable being affected by the independent variable in this case, is life span. Example 2 A scientist studies the impact of a drug on cancer. The independent variable is the administration of the drug. The dependent variable is the impact the drug has on cancer. Example 3 A scientist studies the impact of withholding affection on rats. The independent variable is the affection. The dependent variable is the reaction of the rats. A scientist studies how many days people can eat soup until they get sick. The independent variable is the number of days of consuming soup. The dependent variable is the onset of illness. In mathematics, the x and y values in an equation or a graph are referred to as "variables." If an equation shows a relationship between x and y in which y is specified in terms of x, y is known as the dependent variable and is sometimes referred to as function(x) or f(x). The final solution of the equation, y, depends on the value of x, the independent variable which can be changed. And, never ever forget that slope is calculated most simply by y rise and that the algebraic sign of the x run slope has meaning! Generally, these graphs will be line graphs and will include information collected within a given period of time. This is good news since whenever you see time on the x-axis you have entered the land of rate. You have been solving rate problems for years! If the line on the graph is a straight line, then the slope of the line is simply equal to the rate. If the line is a curve and you are asked about the rate at a given set of conditions represented by a point on the graph, then draw the line tangent to the curve and calculate the slope of the tangent line. 1

2 Data may also be presented logarithmically. A logarithmic scale is a scale of measurement that displays the value of a physical quantity using intervals corresponding to orders of magnitude, rather than a standard linear scale. A simple example is a chart whose vertical or horizontal axis has equally spaced increments that are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4. Each unit increase on the logarithmic scale thus represents an exponential increase in the underlying quantity for the given base (10, in this case). You already know at least three base 10 logarithmic scales: Richter (earthquakes), ph (acids & bases), and decibels (human hearing). If an earthquake of 3 on the Richter scale is compared to an earthquake of 5, most folks understand the earthquake scoring a 5 on the Richter scale is worse than one scoring a 3. However, most folks don t understand the earthquake scoring 5 is 100 times worse since the earthquake scoring 3 since the 3 and 5 are exponents on the base 10 which differ by 2 units, which translates into 10 2, lovingly referred to as 100. Plotting data on a logarithmic scale has many advantages for environmental science. The data within a given set may span many orders of magnitude. For example, concentrations of a particular toxin may be given in parts per million such as 0.02 ppm, 0.3 ppm, 1ppm and 101 ppm. Plotted on a linear scale, the three smallest data points will all be placed practically on top of each other at the origin while 101 ppm would be at the far opposite edge. Perhaps an example you can relate to will help! Sample Problem 1 College students often joke that when a scientist gives a presentation, every mathematical equation shown causes half the audience to stop paying attention. Let's pretend we are at a boring lecture of this type and the scientist giving the lecture has 15 slides. At the beginning of the lecture before any slides are shown, everyone in the audience is paying attention. Each of the 15 slides contains a mathematical equation and each time a new slide is shown, half of the audience tunes out. How many people would have to be in the audience for there to be one person left paying attention at the end? (It's easier to figure this out if you work backwards in time.) Construct a data table and generate two graphs of the data, one on a linear scale and another on a logarithmic scale. Be sure to include a title, label the axes with (units) and since you are plotting discrete data points, please plot them with a symbol and connect the symbols with a line. 2

3 Percent change is also easily interpreted. A change from 7.5 to 10 would be the same distance on the graph as 75 to 100 since both have a 25% change. Sample Problem 2 Examine the graph shown right. The price of gasoline is one factor that can have an effect on the number of highway vehicle miles traveled (VMT). The graph right shows the percentage change of monthly data from one year to the next. (a) What happened to gasoline prices in late 2001 and early 2002? What effect did this have on vehicle miles traveled during the same time interval? (b) In what time period was there a sharp rise in gasoline prices? Summarize the effect this had on vehicle miles traveled during the next 15 months. (c) Summarize the data corresponding to summer of 2003 through summer of In a semi-logarithmic graph, one axis has a logarithmic scale and the other axis has a linear scale. The points have been plotted and the graph has been completed by drawing the line of best fit, labeling the axes, and giving the graph a title. Note that in the title the fact that logs have been used for the survival time data is indicated along with the means for doing this, i.e. "Semi-Logarithmic Plot." The y-axis has been labeled "MST" not "Log of MST" since the numerical values displayed along the axis are survival times and not log values. Since it is impossible to take the log of a physical quantity (mass, volume, etc.) when we deal with the log of the numbers that measure these quantities, we can treat only the numerical value and not the unit of measure. 3

4 Sample Problem 3 The graph below shows the catches of Peruvian anchovy (Anchoveta) from 1950 to This is one of the most important fish stocks in the world and also the one most notorious for its fluctuations, which are associated with the El Niño phenomenon. (a) Identify the period during which the greatest rate of decline in the fish harvest took place. For the five-year period, calculate the rate of decline in the fish harvest, in metric tons per year. Show clearly how you determined your answer. 4

5 Sample Problem 4 According to atmospheric temperature and CO 2 concentration records derived from Antarctic ice cores, Earth s climate has undergone significant changes over the past 400,000 years. Two graphs are shown below. The upper graph show the variation in Atmospheric CO 2 concentration, and the lower graph shows the variation in air temperature. Both graphs cover the same time period from approximately 400, 000 years ago up until the present. (a) Determine the net change in atmospheric CO 2 concentration between 275,000 years ago and 325,000 years ago. (b) Calculate the ratio of the change in mean global temperature to the change in atmospheric CO 2 concentration between 275,000 years ago and 325,000 years ago. 5

6 Sample Problem 5 An experiment is performed to test the toxicity of ammonium hydroxide using crickets as a test organism. Six different concentrations of ammonium hydroxide solution are prepared in separate containers, and 10 crickets are placed in each container. After 48 hours, the number of crickets that have died is counted and recorded. The results of this experiment are shown in the table below. Determine the LD 50 for ammonium hydroxide with respect to crickets. Concentration (%) Number of dead crickets Percent of dead crickets Recorded observations: All but one cricket appears dead. Lone cricket struggling Crickets showing signs of stress. Many mortalities among the population. 1 3 Three apparent cricket mortalities, 7 still alive, unusual abdomen movements Normal activity overall, one cricket appears deceased due to labored respiration Normal activity overall, one cricket appears to be moving much slower than others. 0 0 Normal activity, crickets moving about, making cricket sounds. Plot these data on the blank semi-log graph provided below. Title the graph and label the axes. Draw a smooth curve through the data points to illustrate the overall trend of the data. References: