Understanding graphs and analyzing graphs
- 1. 6th InClass Worksheet Name _________________ Graph Practice Teacher _______________ Due ____________________________________ Making Science Graphs and Interpreting Data Scientific Graphs: Most scientific graphs are made as line graphs. There may be times when other types would be appropriate, but they are rare. The lines on scientific graphs are usually drawn either straight or curved. These "smoothed" lines do not have to touch all the data points, but they should at least get close to most of them. They are called bestfit lines. In general, scientific graphs are not drawn in connectthedot fashion. Here are two examples of bestfit graph lines. One is drawn correctly, the other is not. BestFit Line #1 BestFit Line #2
- 2. · A graph is a visual representation of a relationship between two variables, x and y. · A graph consists of two axes called the x (horizontal) and y (vertical) axes. These axes correspond to the variables we are relating. In economics we will usually give the axes different names, such as Price and Quantity. · The point where the two axes intersect is called the origin. The origin is also identified as the point (0, 0). Initial Practice: Points on a Graph Use the graph below to answer the three questions for this problem. 1. Which point is (0, 6)? 2. What is the ycoordinate of point S? 3. What are the coordinates of point T? Answers: 1. 2. 3.
- 3. Additional Practice: Points on a Graph Use the graph below to answer the four questions for this problem. 1. Which point(s) lie on the xaxis? 2. What is the ycoordinate of point S? 3. What are the coordinates of point Q? 4. What are the coordinates of point T? Answers: 1. 2. 3. 4. Locating Points on a Graph Example 1. Which point is on the yaxis? 2. Which point is labeled (20, 60)? 3. Which point(s) have a y coordinate of 30? Answer: 1. 2. 3.
- 4. Variables and Constants The characteristic or element that remains the same is called a constant. Example: the number of donuts in a dozen is always 12. So, the number of donuts in a dozen is a constant. Other these values can vary (Example: the price of a dozen donuts can change from $2.50 to $3.00). We call these characteristics or elements variables. Variable is the term for any characteristic or element that changes. You should be able to determine which characteristics or elements are constants and which are variables. Practice Example Which of the following are variables and which are constants? The temperature outside your house. This is a ________________________________ The number of square feet in a room 12 feet by 12 feet. This is a ________________________________ The noise level at a concert. This is a _______________________________ Which of the following are variables and which are constants? Price of a gallon of gas. ___________________________ Number of inches in a foot. ___________________________ Number of leaves on a tree. ___________________________ Capacity of the gas tank of your car. ___________________________
- 5. Graphs are a useful tool in science. The visual characteristics of a graph make trends in data easy to see. One of the most valuable uses for graphs is to "predict" data that is not measured on the graph. · Extrapolate: extending the graph, along the same slope, above or below measured data. · · Interpolate: predicting data between two measured points on the graph.
- 6. How To Construct a Line Graph On Paper Step What To Do How To Do It 1 Identify the variables a. Independent Variable (Controlled by the experimenter) · Goes on the X axis (horizontal) · Should be on the left side of a data table. b. Dependent Variable (Changes with the independent variable) · Goes on the Y axis (vertical) · Should be on the right side of a data table. 2 To determine the variable range. a. Subtract the lowest data value from the highest data value. b. Do each variable separately.
- 7. 3 To determine the scale of the graph. a. Determine a scale, (The numerical value for each square), that best fits the range of each variable. b. Spread the graph to use MOST of the available space. 4 Number and label each axis. · This tells what data the lines on your graph represent. Label both the x and y axis. 5 Plot the data points. a. Plot each data value on the graph with a dot. b. You can put the data number by the dot, if it does not clutter your graph. 6 Draw the graph. a. Draw a curve or a line that best fits the data points. b. Most graphs of experimental data are not drawn as "connectthedots". 7 Title the graph. a. Your title should clearly tell what the graph is about. b. If your graph has more than one set of data, provide a "key" to identify the different lines.
- 8. Graphing Practice – Problem 1 Age of the tree in years Average thickness of the annual rings in cm. Forest A Average thickness of the annual rings in cm. Forest B 10 2.0 2.2 20 2.2 2.5 30 3.5 3.6 40 3.0 3.8 50 4.5 4.0 60 4.3 4.5 A. The thickness of the annual rings indicates what type of environment was occurring at the time of its development. A thin ring usually indicates a lack of water, forest fires, or a major insect infestation. A thick ring indicates just the opposite. B. Make a line graph of the data. C. What is the dependent variable? D. What is the independent variable? E. What was the average thickness of the annual rings of 40 year old trees in Forest A? in Forest B? F. Based on this data, what can you conclude about Forest A and Forest B? The dependent variable is ____________________________ The independent variable is __________________________ The average thickness of annual rings of 40year old trees in Forest A was _____________. Forest B was _____________. What does this tell you about conditions in Forest A and Forest B when the trees were 40years old?
- 9. Graphing Practice Problem 2 pH of water Number of tadpoles 8.0 45 7.5 69 7.0 78 6.5 88 6.0 43 5.5 23 A. Make a line graph of the data. B. What is the dependent variable? C. What is the independent variable? D. What is the average number of tadpoles collected per sample? E. What is the optimum water pH for tadpole development? F. Between what two pH readings is there the greatest change in tadpole number? G. How many tadpoles would we expect to find in water with a pH reading of 5.0? The dependent variable is _______________________________ The independent variable is ______________________________ The average number of tadpoles collected per sample is ________ Between pH _______ and pH __________ is the greatest change in tadpole number. If the water’s pH was 5.0, you would expect to find __________of tadpoles.
- 10. Graphing Practice Problem 3 Amount of ethylene in ml/m2 Wine sap Apples: Days to Maturity Golden Apples: Days to Maturity Gala Apples: Days to Maturity 10 14 14 15 15 12 12 13 20 11 9 10 25 10 7 9 30 8 7 8 35 8 7 7 A. Ethylene is a plant hormone that causes fruit to mature. The data above concerns the amount of time it takes for fruit to mature from the time of the first application of ethylene by spraying a field of trees. B. Make a line graph of the data. C. Make a key for the different kinds of apples being graphed. D. What is the dependent variable? E. What is the independent variable? The dependent variable is ________________________________ The independent variable is ______________________________
- 11. Graphing Practice Problem 4 Water Temperature in o C Number of developing clams 15 75 20 90 25 120 30 140 35 75 40 40 45 15 50 0 A. A clam farmer has been keeping records of the water temperature and the number of clams developing from fertilized eggs. The data is recorded above. B. Make a line graph of the data. C. What is the dependent variable? D. What is the independent variable? E. What is the optimum temperature for clam development? The dependent variable is ________________________________ The independent variable is ______________________________ The optimum temperature for clam development is ____________
- 12. Graphing Practice – Problem 5 Time ( seconds ) Distance ( meters ) 0 0 1 2 2 8 3 18 4 32 5 50 6 72 7 98 8 128 9 162 10 200 A. Graph the data. Graphing Practice – Problem 6 The volume of a gas decreases as the temperature of the gas decreases. A sample of gas was collected at 100 degrees Celsius and then cooled. The changes in the volume of the sample are shown below. TEMPERATURE ( o C ) VOLUME ( ml ) 100 317 80 297 60 288 40 278 30 252 20 243 10 236 0 233 10 227 30 202 A. Graph the data.