1 Valor Christian High School Mrs. Bogar Biology Graphing Fun with a Paper Towel Lab I m sure you ve wondered about the absorbency of paper towel brands as you ve quickly tried to mop up spilled soda from your mom s extremely white carpet before she entered the room. Well, today is your chance to find the answer to your problem. Do you think commercials that compare paper towel brands are really fair tests of which brands are actually the best? Could you conduct a fair test? You now have the chance to use the following lab to test your hypothesis. Before you begin you need to decide how you will record your data. Use the following guidelines to evaluate your method of recording data: 1. Communicate the relationship between the independent and dependent variables. 2. Communicate the order in which the independent variable is changed. 3. Communicate the purpose of the experiment in the title. DATA TABLES Here are some other guidelines for constructing a data table: 1. The independent variable is almost always recorded in the left column of the table and the dependent variable is in the right column. 2. When repeated trials are conducted, record them in subdivisions in the dependent variable column. 3. If you have derived quantities (the mean height risen per second of submersion) they need to be calculated and recorded in an additional column to the right. 4. The independent variable data needs to be ordered. 5. You can arrange the data from smallest to largest or visa versa. Most people tend to order their data from smallest to largest. 6. Your title needs to communicate the purpose of your experiment through specific references to the variables being investigated. An example would be The Effect of Submersion Time on an M & M Candy Color Diffusing into Surrounding Water. LINE GRAPHS Line graphs communicate, with picture, the data collected in an experiment. Many people believe that data is communicated better in a line graph than in a data table. If you choose to construct a line graph they do take more work, including understanding the major parts of a graph, relating data pairs from a data table to data pairs on a graph, constructing a good scale for each axis, plotting the data on a graph and then summarizing the trends through descriptive sentences.
2 You begin by drawing and labeling the axes. Graphs are pictorial representations of your data placed on a horizontal and vertical axis. The independent variable is placed on the X, or horizontal, axis (time of submersion) and the dependent variable (amount of color diffused into liquid) is placed on the Y axis. The measurement unit is placed in parentheses next to, or beneath, the variable. Points on a graph are represented by a set of data. The value for the X axis is written first and then followed by the value for the Y axis. The two numbers are separated by a comma. Place both values in parentheses (13, 12). These are also called number pairs in mathematics. What should your scale be for this graph? An easy way to find your scale is to find the range of the data to be graphed. You do this by finding the difference between the smallest and larges values for the variable. To determine the size for each interval, divide the range by 5. This will result in 5-7 intervals, which is a reasonable number of intervals. You ll know you have too many if your graph is crowded and too few make it hard to plot points. After you divide by 5, round the resulting quotient to the nearest convenient counting number. Numbers counted in multiples work the best (2, 5, 10, etc.). Your next step is to develop a scale for each axis using the rounded quotient as the interval that is less than the smallest value to be graphed. You need to end with an interval that allows the largest value to be graphed. Here are some examples for line graphs:
3 You may find experiments that begin with a data set that is not anywhere near 0. You can begin at a closer number if you like. Remember that all experimental data is subject to error. Because of this, data points on a graph are not directly connected. Instead a line-of-best-fit is used to communicate the general data pattern. To construct this you need to draw a line about which an equal number of data points fall to either side. If you want a more precise line you can use a graphing calculator. Another way is to draw a line so that the sum of the distances of the points above the line to the line is equal to the sum of the distances of the points below the line to the line. Steps for drawing the line of best fit 1. Calculate the "mean point" by finding the average for each variable. o add all entries for the variable on the x axis and divide this sum by the number of data o add all entries for the variable on the y axis and divide this sum by the number of data 2. Plot the mean point on the scatter plot. 3. Draw the line of best fit going through the mean point. Ensure that there is an equal distribution of points above and below the line. The line does not always have to go through the origin (0, 0). Use your common sense to determine when that is the case. Remember: The line of best fit must follow the trend. It goes up if the data show a positive correlation. It goes down if the data show a negative correlation.
Here are some examples of Lines-of-best-fit: 4
5 To summarize this information you will write a sentence that communicates what happens to the dependent variable as the independent variable is changed, e.g., When the amount of time an M & M was in water increased, the diffusion of the color coating into the water also increased. BAR GRAPHS Observations and measurements of variables can be classified as either discrete or continuous. Discrete data are categorical or counted like days of the week, gender, kind of animal, brand of paper towel, number of children or color. Bar graphs are appropriate for these types of variables. Other variables are continuous and are associated with measurements involving a standard scale with equal intervals. Some examples of these are height of plants in centimeters, the amount of fertilizer in grams, and the length of time in seconds. When the data may be any value in a continuous range of measurements, a line graph is a better way to show this data. Line graphs also allow you to infer the value of points on a graph that were not directly measured. One way to figure out which graph is best for you is to see if the intervals between recorded data have meaning. If they do then a line graph is good. When they don t have meaning, like brands of products, then a bar graph is the best way to go. Some examples of bar graphs are shown below:
6 Mean The mean of a list of numbers is also called the average. It is found by adding all the numbers in the list and dividing by the number of numbers in the list. Example: Find the mean of 3, 6, 11, and 8. We add all the numbers, and divide by the number of numbers in the list, which is 4. (3 + 6 + 11 + 8) 4 = 7 So the mean of these four numbers is 7. Median The median of a list of numbers is found by ordering them from least to greatest. If the list has an odd number of numbers, the middle number in this ordering is the median. If there is an even number of numbers, the median is the sum of the two middle numbers, divided by 2. Note that there are always as many numbers greater than or equal to the median in the list as there are less than or equal to the median in the list. Example: The students in Bjorn's class have the following ages: 4, 29, 4, 3, 4, 11, 16, 14, 17, 3. Find the median of their ages. Placed in order, the ages are 3, 3, 4, 4, 4, 11, 14, 16, 17, 29. The number of ages is 10, so the middle numbers are 4 and 11, which are the 5th and 6th entries on the ordered list. The median is the average of these two numbers:
7 (4 + 11)/2 = 15/2 = 7.5 Mode The mode in a list of numbers is the number that occurs most often, if there is one. Example: The students in Bjorn's class have the following ages: 5, 9, 1, 3, 4, 6, 6, 6, 7, 3. Find the mode of their ages. The most common number to appear on the list is 6, which appears three times. No other number appears that many times. The mode of their ages is 6. PAPER TOWELS AND ABSORPTION RATES Problem: Hypothesis: Materials: Paper towels Brands A, B, C 250 ml beaker Water Graduated cylinder (100 ml) Timer Pencil Procedure: 1. Measure 100 ml of water with the graduated cylinder. Add the water to the beaker. 2. Obtain one square of the paper towel brand designated by your teacher, such as Brand A, B, or C. 3. Push the square of paper towel into the water for 30 seconds. Use a pencil to push the towel under the surface. 4. Remove the paper towel. Hold the paper towel over the beaker until it stops dripping. 5. Use the graduated cylinder to measure the amount of water (ml) remaining in he beaker. Subtract the value from 100 ml to determine the amount of water (ml) absorbed by the towel. 6. Repeat Steps 1 to 5 for a total of 4 trials. 7. Repeat Steps 1 8 for the other two brands of paper towel. 8. Calculate the average amount of liquid absorbed (ml) for each brand. Construct data tables (one for each brand) using the following guidelines:
8 1. Make a table containing vertical columns for the independent variable, dependent variable, and derived quantity (average water absorbed). 2. Subdivide the column for the dependent variable to reflect the number of trials. 3. Record the values of the independent variable (Brands A, B, and C). 4. Record the values of the dependent variable that correspond to each value of the independent variable. 5. Calculate the derived quantities and enter the values into the table. Construct a bar graph from the data using the following guidelines: 1. Draw and label the X and Y axes of the graph. 2. Write data pairs for the values of the independent and the dependent variable; use the derived quantity (average water absorbed) recorded in the data table. 3. Subdivide the X axis to depict the discrete values of the independent variable, three paper towel brands. Evenly distribute the values along the axis, leaving space between each value. 4. Determine an appropriate scale for the Y axis that depicts the continuous values of the dependent variable, water absorbed (ml); subdivide the Y axis. 5. Draw a vertical bar from the value of the independent variable on the X axis to the corresponding value of the dependent variable on the Y axis. Leave spaces between each bar. 6. Summarize the data trends with descriptive sentences. If you have a graphing calculator, you can also do the following: 1. In the STAT mode of your calculator, enter consecutive numbers (e.g., 1, 2, 3.) for the brands of paper towel in List 1 and the values for amount of water absorbed in List 2. 2. In setting up your graph, select histogram (bar graph) as your graph type and List 1 for you x values and List 2 as the frequency. Graph the data. Depending on the brand of your calculator you may have the option to adjust the spacing and width of the bars. *discrete data data that exists in categories that are separate and do not overlap such as brands of products and kinds of papers. When displayed by a scale on a graph, the points between the defined categories do not have any meaning. Discrete data can be graphed as a bar graph, but not a line graph. *independent variable the variable that is changed on purpose by the experimenter. *dependent variable the factor or variable that may change as a result of changes purposely made in the independent variable.