2. Graphing Practice. Warm Up

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1 2. Graphing Practice In this worksheet you will practice graphing and use your graphs to interpret and analyze data. The first three questions are warm-up questions; complete this section before moving on to the other practice examples. If you need more support with graphing skills, you can watch Mr. Anderson s videos on graphing. (a) Beginner s Guide to Graphing Data: (b) Graphing Data by Hand: (c) Graphing Data by Spreadsheet: Again, make sure you can answer the first three questions before beginning the Further Practice section. Answers for the Warm Up questions are provided so you can check your work. Warm Up 1. The following are five different types of graphs. For each type, give an example of a data set that you could use the graph for. (i) Pie chart (ii) Line graph (iii) Histogram (iv) Scatter plot (v) Bar graph 2. True or False: Determine whether the statement is true or false. Explain your answers. (a) The best title for a graph is a short, simple title that doesn t take too long to read. (b) It is okay to put the dependent variable on either the x- or y-axis, depending on where it looks better. (c) The units of measurement should always be included in an axis title (i.e. Tree Height (meters) ). (d) In a scatter plot the best-fit line should include an arrow head to indicate that the trend might continue. (e) The number values on the grid marks of a graph should always be equally spaced even if they aren t the same as the values of the data points. (f) The number 0 should always be included for reference on the axes in a graph. (g) An axis should always have more than one value on it for comparison.

2 3. The following data table 2 shows the total number of tornadoes occurring in the United States for each year between 1980 and It also shows the number of deaths per year from the tornadoes. Year Total # of Tornadoes Number of Tornadoes by Month Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec Create the following graphs for this data set by hand. After creating each graph, describe what information you can observe from your graph. (i) A scatter plot that shows the correlation between the number of tornadoes per year and the number of deaths per year. (ii) A line graph that shows the number of tornadoes each year between 1980 and (iii) A pie chart that displays proportion of tornadoes by month for the year After creating those graphs, consider the following questions (iv) What data from this set could you arrange into a bar graph? (v) What data from this set could you arrange into a histogram? Total # of Deaths 2 The data set is taken from mathforum.org on the Data Sets page (located in spring 2014). The link is

3 Warm Up Solutions 1. Data set examples will vary. (i) A pie chart is useful when proportions of a whole are being compared. For example, if multiple phenotypes were being investigated, a pie chart could show the proportion of the population that has each given phenotype. (ii) A line graph is most useful to show change over time. One might plot the number of flowering plants over time to see how they respond to different seasons. (iii) When counts in different numerical categories are being compared, a histogram is useful. For example, the number of students in your school who are in different height groups (i.e , > , etc.) could be plotted in a histogram. (iv) A scatter plot can be used to visualize whether there is correlation between two different data sets, particularly if the data sets are numerical. One could graph plant height versus direct sunlight hours each day provided in an experiment. (v) A bar graph is best for comparing numerical values between groups. Such a data set might be the percentage of population living below the poverty line across countries. 2. (a) False. A title should contain the entire story of what is contained in the graph. (b) False. The dependent variable always belongs on the y- or vertical axis. This is standard and allows people to know which variable depended on the other when looking at a graph. (c) True. If the units are included, a reader of the graph could misinterpret the results. (d) False. The line of best fit only applies where data was collected so no arrow head should be included. (e) True. This gives a true comparison between points on the graph. (f) False. The number 0 may lie far out of the range of the graph values. It is better to scale the graph appropriately to give the most information. (g) True. Graph scales are relative to other values on the graph, so more than one is needed in order to understand the information. 3. For ease of electronic distribution, excel versions of the graphs are provided. (i)

4 (ii) (iii) (iv) Answers may vary. One possible bar graph set is the average number of tornadoes over the years given by month. (v) Answers may vary. One could graph the distribution of number of tornadoes over these years in a given month, for example, the distribution of total number of US tornadoes in August over these years.

5 Further Practice 1. Consider the data set contained in the excel file tv.xl.zip.xls 3. It contains average life expectancy data, by country, from the 1993 World Almanac and Book of Facts. For each country, you will see lists of the number of people per television set, the number of people per physician, and a break-down of the total life expectancy into the averages for female and male. Create the following graphs for this data set: (i) A scatterplot showing the correlation between average life expectancy and the number of people per television. (ii) A scatter plot showing the correlation between average life expectancy and the number of people per physician. (iii) A bar graph showing the number of people per physician per country. After creating the graphs, describe what information you can observe from your graph. Consider the following questions: (iv) Is there data that could be arranged into a line graph? Why or why not? Explain your answer. (v) Is there data that could be arranged into a histogram? Why or why not? Explain your answer. 2. In AP Biology Lab Investigation #1, you explore artificial selection in consideration with plant trichomes. The following table lists the trichome count of 30 different plants, similar to the plants you worked with in the investigation. Use the data to complete the following tasks: Plant # Trichome Count Plant # Trichome Count (a) Create a histogram of the data that indicates the number of plants grouped by trichome counts between 1&10; 11&20; 21&30; etc. What information could you infer from looking at this graph? (b) Create a line graph for this data in which you plot the trichome count versus the plant number for each of the plants counted. Explain whether or not you find this graph useful and why. 3. In AP Biology Lab Investigation #7, you examine onion root tip cells undergoing mitosis. An image from your lab manual is included in Figure 1. Use this image of onion root tip cells in various stages of cell division in order to answer the following questions: (a) Count the number of cells in the photo that are in interphase or mitosis. Because we are using an image, it is okay to include an unknown group, for those cells that cannot be sorted into a definite stage. (b) Based on your cell counts, create a pie graph that shows the proportion of cells in each phase. (c) Explain why a scatterplot would not be a good way to group the data here if we are interested 3 The data set is also taken from mathforum.org and can be found on the Data Sets page.

6 in the proportion of cells in each phase. Figure 1. Onion root tip cells in various stages of mitosis. 4. Because the onion tips in Investigation #7 are so interesting, so you continue investigating with your own questions and hypotheses. In particular, you are curious if the lab temperature affects the number of cells undergoing mitosis. With your lab partner you collect the following data over several days with lots of different onion root tips: Temperature (F o ) Proportion of Mitotic Cells (a) Create a scatterplot of the proportion of mitotic cells versus the temperature. Make sure you can explain why we would use a scatterplot instead of a line graph. (b) Does the graph you created suggest there might be a relationship between temperature and mitotic rates? Why or why not?