GRAPHING AND INTERPRETING DATA Regents Biology

OBJECTIVES Upon completion of this unit students will be able to:    1. Explain the purpose of tables and graphs. 2. Explain how to properly organize and construct a table.   3. Correctly identify where to find the dependent and independent variables on graphs and tables. 4. Make an appropriate scale on each axis of a graph. 5. Correctly plotting, connecting and circling points on a graph. 6. Differentiate between point-to-point graphs and best-fit curves. 7. Evaluate poorly constructed and properly constructed graphs.

KEY TERMS Independent Variable Dependent Variable Point-to-point Graph   KEY TERMS Independent Variable Dependent Variable Point-to-point Graph Graph Table Scale Interpret Best-fit Curve Axis  

I.INTRODUCTION The Regents Exam that you will take in JUNE will contain many tables, diagrams and graphs. This unit is meant to help you learn how to construct, analyze, and interpret graphs and tables. Tables and graphs provide a concise summary of data and relationships. If they are well-constructed, TITLED AND LABELED, they are self-explanatory and can stand by themselves. However, if they are poorly constructed, either the reader will not understand them or they will have to be described in detail in the text, thus defeating the purpose.

Q: What is the purpose of tables and graphs? A: TO PROVIDE A CONCISE SUMMARY OF DATA AND RELATIONSHIPS

II.CONSTRUCTION OF TABLES Clear, concise data tables convey a wealth of information in a convenient, easy to understand way. Guidelines: Each table should have a NUMBER AND A TITLE that briefly states what data are involved. Tables should be constructed so that they read DOWN, not ACROSS. Compare Table 1A and Table 1B.

Table 1A. Common Characteristics of Several Domestic Cats Table 1B. Common Characteristics of Several Domestic Cats Table 1A. Common Characteristics of Several Domestic Cats   Siamese Calico Tiger Burmese Persian Fur Color Grey Orange Brown White Eye Color Blue Green Stripes? No Yes Average Weight (lbs.) 5 lbs. 6 lbs.   Fur Color Eye Color Stripes? Average Weight (lbs.) Siamese Grey Blue No 5 lbs. Calico Brown 6 lbs. Tiger Orange Green Yes Burmese Persian White Table 1A reads across, and Table 1B reads down. It is obvious which table is easier to read. This construction is even more important when NUMBERS are involved because we are trained to add numbers VERTICALLY, not HORIZONTALLY. Table 1A reads across, and Table 1B reads down. It is obvious which table is easier to read. This construction is even more important when NUMBERS are involved because we are trained to add numbers VERTICALLY, not HORIZONTALLY.

III.CONSTRUCTION OF GRAPHS Graphs are a very effective method of describing results. They depict RELATIONSHIP between values plotted on the y-axis (the ordinate – VERTICAL AXIS) and the x-axis (the abscissa – HORIZONTAL AXIS) THE Y-AXIS SHOULD ALWAYS LIST THE DEPENDENT VARIABLE AND THE X-AXIS SHOULD ALWAYS LIST THE INDEPENDENT VARIABLE.

Q: How do you know which is which? A: Ask yourself the question--“Which variable is DEPENDENT ON THE OTHER?” In other words, which one relies on the other? Let’s say that you have two variables----time and child height. TIME is the independent variable and CHILD HEIGHT is the dependent variable.

1. You want to show the relationship between the level of photosynthesis and light intensity. The photosynthetic level is the DEPENDENT VARIABLE since it depends on the independent variable, which is LIGHT INTENSITY. If you plotted light intensity as the dependent variable the graph wouldn’t make sense. Then you are saying that if you increase the photosynthetic level of the geranium on your window sill, the sun up in the sky will shine brighter! One excellent example of an independent variable is TIME. It is one variable we have no control over and all processes are a function of it. Therefore, it will always be plotted on the X-AXIS.

PHOTOSYNTHETIC RATE as a function of LIGHT INTENSITY   TITLE OF THIS GRAPH: PHOTOSYNTHETIC RATE as a function of LIGHT INTENSITY (ALWAYS DEPENDENT VARIABLE as a function of INDEPENDENT VARIABLE)

2. You must construct your graph so that it tells the whole story of what happened during the experiment in the simplest and most logical manner.   a. Title b. Axes – These should be LABELED as to magnitude, direction and unit using a logical format. For example, if your data goes from 2 to 23, don’t label your axis from 1-100, thereby scrunching the points into a small corner; 0-25 would be much more practical. Also, each square on the graph must always equal a constant amount—EACH SQUARE MUST EQUAL THE SAME AMOUNT OF UNITS!!!

c. Multiple graphs – If two or more data sets are included on a single graph, each must be identified. This is done by using a LEGEND OR KEY, which identifies what the symbols representing different experiments mean.

Quick Review:  1. Name the dependent variable: POPULATION OF DEER (THOUSANDS) 2. Name the independent variable: TIME (YEAR) 3. What would the title of this graph be? POPULATION OF DEER AS A FUNCTION OF TIME 4. In what year did the carrying capacity of the deer begin to go down and why? 1925 BECAUSE THERE WERE TOO MANY DEER AND THE CARRYING CAPACITY HAD BEEN MET AND THE RESOURCES WERE LIMITED  

3. Best fit vs. point-to-point graphs – A graph is accurate of the data points are each connected with a line. However, sometimes this method gives the “TRUTH” but not the “WHOLE TRUTH”. If there is a consistent relationship, this should be shown by means of a best-fit curve. Not only does this illustrate the trend, but it also enables us to make predictions.

GRAPH 1A GRAPH 1B Compare graph 1A and graph 1B. They show two different ways of graphing the relationship between the length of a mammal’s femur and running velocity. Both show that velocity increases with an increase in femur length. However, if we found a 25 cm femur and wanted to estimate how fast the animal could run, we could not use graph 1A. The only way to make a proper estimate is to draw a best-fit curve (graph 1B).

There are some complicated statistical techniques that one must use to produce a truly accurate best-fit line, but we’ll leave those explanations to the statistician for now and use the old stand-by, “the closest to the mostest.” Having drawn the best-fit curve by eye, it is possible to predict the running velocity of the mammal with the 25cm femur. What would it be? ABOUT .7 m/sec