California State University East Bay Biology Lab Worksheet

Data and Graphing Lab on-line Objectives: • • • Review some common terminology used in data collection, analysis and graphing. Learn about different types of data and graphs. Choose and prepare graphs to analyze data sets appropriately. Collecting and analyzing data are important steps in scientific studies. We need to analyze data to understand the world around us. Graphing is one very effective way to analyze and interpret data. A graph is a visual representation of data that shows a relationship between two or more quantities. A good graph shows data more clearly and meaningfully than a simple list or table of numbers. Graphs can show patterns and trends and help summarize information to make it more easily and quickly understood. Graphs may use points, lines, a coordinate system, numbers, symbols, words, shading and color to explain the results of an inquiry. In order to design good graphs, you must be able to choose the appropriate type of graph for particular data set and you need to be familiar with the language and standards of graphing. A good graph clearly shows data, does not distort, and allows the reader to easily understand the results. Data – items of numerical and/or text information. Data can be displayed in lists or tables, or in graphs. The word ‘data’ is actually plural. The singular form of data is ‘datum.’ Average or Mean – “middle” or typical observation of a data set. Average is calculated by summing a group of numbers and dividing the sum by the number of observations. Average of 3, 5, 4 and 2 is: (3 + 5 + 4 + 2) 14 = = 3.5 4 4 Graph – any visual representation of a data set. Common types are pie chart, bar graph, line graph, and scatterplot, but there are many other types. Variable(s) – Categories in data sets are called variables because they change or vary. Anything that is measurable or that can be described can be a variable. For example, in a data set on rose plants, variables might be flower color, stem height, length of petals, number 1 of leaves, number of thorns, etc. Each of these variables would vary from plant to plant. In a relationship between time and temperature, both time and temperature are variables. Time steadily advances while temperature can increase, decrease or remain constant. In most relationships between 2 variables, one variable is considered independent and one is dependent. In a time-temperature relationship, the temperature may depend on the time, but it is not true that time depends on temperature; time advances regardless of other effects. Therefore time is considered the independent variable. In this case, temperature is considered the dependent variable because the temperature depends on time. When making a graph, the independent variable is plotted on the x-axis (horizontal), and the dependent variable is plotted on the y-axis (vertical). Though it may be easy to understand, in the time/temperature relationship, which is the independent and which is the dependent variable, the distinction is not always obvious. In complex systems there can be multiple variables that can be closely related and constantly changing – for example, multiple variables in the US economy. In science however, we usually attempt to control as many variables as possible to focus on only one or two variables we are investigating. Generally, when two variables are being studied, the independent variable is the one that you are controlling or manipulating. Time is often considered as the independent variable too. The dependent variable is the one that is then seen to change, presumably in response to your manipulation, or to time. Remember that by convention, the x-axis is used for the independent variable, while the y-axis is used for the dependent variable. When the variables are changing in the same direction, they are said to have a direct relationship (i.e. when one goes up the other goes up as well). If they are changing in opposite directions, they have an inverse relationship (i.e. when one goes up the other goes down). Types of Graphs There are many different types of graphs used to describe and interpret scientific data. Some of the more common types are pie, bar, line and scatter graphs. 2 Pie chart – a circular graph, cut into colored, shaded or labeled wedges or slices. Pie charts are used primarily for data that adds to 100%. The size of each pie slice is proportional to the percentage of the total it represents. This pie chart example shows the proportion of students receiving A, B, C, D and F grades on an essay assignment. The size of each pie slice is proportional to the fraction of the class receiving that grade. The slices are different colors so it’s even easier to understand. Bar graph – displays data as bars or columns arranged vertically or horizontally. The bar length corresponds to its numerical value. Bars may be grouped or ungrouped. A bar graph is often used to display data from 2 or more distinct, unrelated or non-numerical categories or groups on the xaxis. For example, this bar graph shows student academic performance in 4 separate subjects (math, reading, writing and learning) at 2 different points in time (represented with different colors). 3 Line graph – each point represents one data point or observation and consecutive points are connected with a continuous line. A line graph is often used to show how some quantity changes with time or with another numerical independent variable. At each point on the x-axis, there is only one data point. Connecting the points with a line implies that the points are related to each other in some way. Perhaps the points are multiple measurements taken on the same or similar individuals over time, or in response to an independent variable. Line graphs may have one or more minima (lowest point) or maxima (highest point). We will make use if line graphs quite a bit in this course. This line graph shows the number of medical technologists licensed by the American Society for Clinical Pathology in the US from 1960 to 2002. A maximum number of MTs were licensed in 1978 and a minimum were licensed in 2001. Scatter graph – used to look for a relationship between two numerical variables. Data points usually represent measurements from separate or unrelated individuals. There may be more than one data point on the same point on the xaxis. The scatter graph at the right shows a fairly strong direct relationship between predicted and actual temperatures for 16 different days. 4 ASSIGNMENT: For each of the following data sets, graph the data appropriately, and answer the questions. Submit as required by your instructor. Graph paper, if used, is available in this handout. 1. Attendance and grade data for 45 students in 2 sections of Biol 121 during 2009. Student ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 No Classes Attended (of 29) 27 28 28 23 15 28 27 25 28 22 26 28 24 28 27 28 27 28 22 28 6 28 26 Final Grade (%) 80.1 84.4 94.9 60.0 26.7 93.5 87.1 93.1 90.0 40.4 91.2 73.2 86.1 91.5 85.1 81.5 71.0 96.6 71.6 98.9 15.3 80.5 71.9 Student ID 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 No Classes Attended (of 29) 28 25 28 28 23 16 29 27 29 29 29 22 10 29 27 9 29 20 17 29 28 29 Final Grade (%) 92.7 67.2 94.7 88.7 53.2 53.1 89.9 82.0 83.2 91.0 91.0 69.4 9.9 88.3 67.5 5.9 74.0 37.6 35.3 94.8 94.5 86.2 2. American Red Cross data for the percentage of ABO blood types among 4 United States ethnic populations is shown below. Blood Type A B White 40 11 Black 26 19 5 Hispanic 31 10 Asian 28 25 Blood Type AB O White 4 45 Black 4 51 6 Hispanic 2 57 Asian 7 40 7 8 9 Complete and Turn In for Graphing Lab Credit! You can either scan in your graphs, or complete similar graphs using Excel, Word, or a similar program Name: 1. Biology 121 Student Data a. As you graph the data remember to: clearly label axes and parts of your graph, and make sure your graph has a title. Indicate units where appropriate. Which graph type did you choose? Why? b. What two variables did you graph? c. Which is the independent variable? d. Which is the dependent variable? e. Do the variables demonstrate a relationship? If so, is it a direct or inverse relationship? f. How would you interpret this data? Draw one or two conclusions from your data and graph. g. Evaluate your graph(s). Is it a good graph? Why or why not? 10 American Red Cross Data a. As you Graph the data Remember to: clearly label axes and parts of your graph. Indicate units where appropriate. Which graph type did you choose? Why? b. What two variables did you graph? c. Which is the independent variable? Dependent variable? d. How would you interpret the data? Draw one or two conclusions from your data and graph. e. Evaluate your graph(s). Is it a good graph? Why or why not? 11

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