Data Tables and Graphs PDF

DATA TABLES AND GRAPHS OBJECTIVES By the end of the lab you should be able to: organize and label data into a data table draw a bar graph, line graph, pie chart, and scatter plot distribution analyze data and interpret trends from various graphs INTRODU...

DATA TABLES AND GRAPHS OBJECTIVES By the end of the lab you should be able to: organize and label data into a data table draw a bar graph, line graph, pie chart, and scatter plot distribution analyze data and interpret trends from various graphs INTRODUCTION “A picture is worth a thousand words”. Tables and graphs can show a lot of information in an organized and concise manner. We will practice drawing and interpreting data tables, bar graphs, line graphs, pie charts and scatter plots. The basic rules for tables and graphs include: Keep tables and graphs simple. Use a title that summarizes the purpose and content of the data table or graph. Label all measurement units. Label all components (axes, columns, rows, lines) directly. If needed, use separate legend key as needed. Fig 1. Bill Length in English Sparrows 20 DATA TABLES 18 A data table is used to summarize information in an 16 organized fashion. Tables are usually displays of 14 numbers, but can also be used for short phrases. One Number of Birds 12 or several parameters (features) could be included in 10 the same data table. 8 6 The basic format for data tables should: 4 have a title that summarizes the purpose and 2 content of data table 0 display columns and rows of numbers 5-6.9 7-8.9 9-10.9 11-12.9 13-14.9 label measurement units Bill Length (mm) present data in logical order include statistical significance, definitions, and extra information at the bottom. Suppose researchers are interested in the feeding habits and variations of English sparrows. They measured the bill length of thirty birds and compiled the numbers in Table 1. This list is called “raw” data because the data has not been organized yet. ORGANIZING THE DATA. At a glance, it is difficult to look at Table 1 and determine what size bill most birds have, or whether there are more smaller or larger bills. For easier analysis of the data, the measurements need to be placed in categories of different sizes. Count the number of birds that fit into each 1 mm category and fill in Table 2. The second row is for tally marks, the third row is for your final answers. Be sure to write a descriptive title for Table 2. Biology 101 Lab Data Tables and Graphs – 1 Table 1. English Sparrow Bill Length Data - in order collected. Indiv Length (mm) Indiv Length (mm) Indiv Length (mm) Bird 1 10 11 11 21 12 2 9 12 6 22 11 3 11 13 9 23 10.5 4 12 14 10 24 10 5 8 15 10.5 25 11 6 11 16 14 26 13 7 11.5 17 11 27 10 8 10.5 18 8 28 14 9 13 19 12 29 7 10 12 20 11.5 30 7 Table 2. _______________________________________________ Length (mm) 5-5.9 6-6.9 7-7.9 8-8.9 9-9.9 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9 # Birds (tally) # Birds STATISTICAL ANALYSIS Calculate the values for Statistics Statistics Definition the bird bill data. Term Mean (average of all data points). Add all the individual data points and then divide by the total number of measurements. Range (difference between the smallest and largest data points). Median (middle data value). Place the data numbers in order from least to greatest, and find the number in the middle. Mode (number or numbers that occur most often). BAR GRAPHS The information contained in the table is now used to create a graph. Bar graphs are used when the data is grouped into ranges or categories. A bar graph consists of an axis and a series of labeled horizontal or vertical bars that show different values for each bar. A bar graph can show a single set of data or provide comparison of several sets of data. The vertical bar graph is used most often. But a horizontal bar graph is acceptable and allows more room for labeling each individual bar. The numbers along a side of the bar graph are called the scale. Refer to the graph in Figure 1: Bill Length in English Sparrows. All graphs contain an independent axis on the x- axis (horizontal). The independent axis contains the variable data that you choose to measure. In the above example, we chose to measure bill length. Therefore this information goes on the horizontal axis that must be labeled with the “Bill Length” information it measures. The lines of the graph must be labeled with the numbers that represent the categories of bill length. These numbers must be evenly spaced, as are the categories on Figure 1. Note that next to the label for the axis there is a note of the units of measurement used to get the numbers; in this case, mm for millimeters. Biology 101 Lab Data Tables and Graphs – 2 The Y-axis (vertical axis) is the dependent axis and contains the information that results from our choice of measurement on the independent axis. The number of birds with particular bill lengths depends on the measurement of the bills and therefore is the dependent variable. Again, the vertical axis must have evenly spaced numerical categories of number of birds, a label of what it is measuring and the units of measure. In this case the word “number” in “Number of Birds” serves as the units. The value of the dependent variable is determined by and is a function of the independent variable. In an ideal experimental setup, the independent variable is something that we have some control and changes in some predetermined way while changes in the dependent variable are observed. The actual data that we collect is displayed on the graph as darkened areas to indicate the number of birds in each bill length category. The first bar is drawn even with the number 5 on the dependent axis to show that 5 birds had bills within 5.0 - 6.99 mm. When completed, the graph is titled in such a way that a reader may understand what was measured and, therefore, what the data means. Directions: Using Table 2 that you created with bill length categories of 1 mm, draw and completely label a bar graph of the data (Figure 2). Use Figure 1 as an example, but obviously, DO NOT COPY IT exactly. Be sure to use a descriptive title, label the axes and appropriate units. Figure 2. _________________________________________________ Biology 101 Lab Data Tables and Graphs – 3 INTERPRETING BAR GRAPHS Fig 3. Bio 101 Grades Look at Figure 3: Bio 101 Grades. 3a) What is the independent variable? 18 16 _________________ Number of Students 14 12 10 3b) Which axis contains the independent 8 variable? ______ 6 4 2 3c) How many “A” letter grades were given 0 A B C D F to students? ______ Letter Grades Blood Type Differences in 3 Populations A double bar graph (or grouped bar graph) is similar to a vertical bar graph, but gives two (or more) pieces of information for each Europeans Americans Dunkers item on the vertical axis, rather than just one. 70 Grouped or stacked bar graphs also depict Percent of Population 60 comparisons that are easy to understand. 50 40 Look at Figure 4: Blood Type Differences in 30 Three Populations 20 10 4a) Which group had the lowest frequency of 0 Type A blood? ________________ A B Rh M MN N Blood Types 4b) Which blood types were more common in Dunkers than in Americans? __________ Look at Figure 5. Average Tuition at CSUF and UCI. http://images.onset.freedom.com/ocregister/article/m3pzo0- m3pznrtuitionatuccsus.jpg 5a) How much was the UCI tuition in 2011- 2012? ____________________________ 5b) Compare this graph to the other bar graphs. What two labels are missing in this figure? _______________________________ _______________________________ Biology 101 Lab Data Tables and Graphs – 4  Data can also be represented with a Look at the grouped horizontal bar graph in horizontal bar graph. Fig 8: Fruit Sold on Sept 1-2. Fig. 6. Origins of Immigrants to Canada Fruit Sold on Sept 1-2 Apples Oranges 1-Sep Fruit 2-Sep Mangoes Star Fruit Papaya 0 50 100 # kilograms 6a) In this horizontal bar graph, which is now the dependent axis? ______________ 8a) Which fruit had the most sales (by weight) on Sept 1? _______________ 6b) What is the dependent variable? __________________________________ 8b) Which fruit had the worst sales on both days? ______________ Fig. 7. The same data can also be represented as a stacked or composite bar graph (either horizontal or vertical). In this case, the sum for each category is shown. Fig 9. Stacked bar graph of Fruit Sold Fruit Sold on Sept 1-2 Apples Oranges Type of Fruit Mangoes 1-Sep Star Fruit 2-Sep Papaya 0 50 100 150 # kilograms 7) According to this horizontal graph, what are the top two fastest growing jobs? 9) Which fruit had the best total sales for the _____________________________ two days combined? _____________ _____________________________ Biology 101 Lab Data Tables and Graphs – 5 IV. LINE GRAPHS A line graph is a way to summarize how two (or more) pieces of information are related and how they vary depending on one another. It can compare similarity of two or more groups; show trends and patterns, and the highs and lows of the data. Line graphs are used when there is a connection between consecutive data points, often over a time-period. Possible uses are growth rates, heating rates, temperature changes. Data points can be connected to show that there are changes in between the data points that are important to the interpretation. Line graphs must contain all of the appropriate parts of a graph: a title, a dependent axis and an independent axis numbered in a linear fashion, and the units of measurement for both axes. In addition, the graph must also contain a legend key to allow the reader to distinguish between the two data sets (and special markings). Basic format of Line Graphs: Label the X and Y axes with title and units Y axis should be about 3/4 or same length as X axis Y axis scale starts at zero, X-axis scale does not have to have at zero Figure 10. California Public University Tuition According to the graph in Figure 10, removing inflation and using current dollar values, what was the cost of UC tuition in 1970: $_____________ 1990: $_____________ 2010: $_____________ Fig 11. Genetically Engineered crops in US (1996 - 2006). http://www.agronomy.unl.edu/biotechnology/biotechnology_graph.jpg In 1997, what per cent of US farm acres with soybean crops were raising genetically engineered soybeans? In 2006, what per cent of US farm acres with soybean crops were raising genetically engineered soybeans? Biology 101 Lab Data Tables and Graphs – 6 V. PIE CHARTS A pie chart is a circle graph divided into pieces, each displaying the size of some related piece of information. Pie charts visually displays the proportion (or sizes) of parts that make up some whole, and must be drawn to scale. Try to limit to about 6 “slices” of pie, or the pie chart will be too cluttered. Fig. 12. Home counties of 3900 Freshmen entering CSUF in 2005. How many students came from Orange County? __________________ About 310 students came from one county to CSUF. Which county? ________________ Fig 13. In 2007, US families spent $47.3 billion dollars for “Back to College” purchases. That is an average spending of $956.93 per student. Calculate what per cent was spent on: Textbooks __________% Housing ___________% Shoes ____________% Ref: http://www.webadvantage.net/webadblog/last- minute-online-marketing-tactics-for-back-to-school- advertising-520 Composition Mushroo of a 600g Pizza Fig 14. Composition of a 600 gram Pizza. ms Tomato 5% Determine the weight of each ingredient in the 7% 600 gram Pizza from the given pie chart. Sausage 13% Crust Ingredient: 50% Cheese ____________g Cheese 25% Mushrooms ________ g Biology 101 Lab Data Tables and Graphs – 7 Scatter Plots The two previous graphs (bar and line) graphically depicted the results of observations (dependent variables) vs. some units of measure (independent variables). Sometimes when we are looking for relationships, we need to record two dependent variables per test result. A very useful type of graph to look for relationships between two dependent variables is a scatter plot. In this case, each of the dependent variables is given its own axis. You choose which variable to place on the vertical axis and on the horizontal axis. After plotting the data points, you can then try to determine if there is in fact a relationship. To show a relationship on a scatter plot, a line is the obvious choice. Since there can be two individual samples that share one variable but differ on the other, and since there is no connection between two individual samples, we cannot simply connect the dots to make our line. We use a method called “best fit curve”. In this case, the line is drawn so as to best fit the scattered data points. This is sort of an average of the points. If the “best fit curve” is a smooth straight line that intersects almost all the points, this is an indication that there is a strong relationship between the variables. If the “best fit curve” is a wild approximation, this is an indication that there is little or no relationship between the variables. The further the data points are from the “best fit curve”, the less likely the relationship. Most computer graphing programs will automatically draw the “best fit curve”. DIRECTIONS: Draw the best-fit curve (straight line) for each of the following scatter plots. Describe the relationship (positive, negative, or no relationship) between the two variables. 15. 16. 17. 19. 18. Biology 101 Lab Data Tables and Graphs – 8 GRAPHING REVIEW. The Growth of Shaquille O'Neal. One of the most famous 'big' basketball players is Shaquille O'Neal, the 'Shaq'. Here is a list of his growth from age 4 to adult. Choose one trait and make a graph using Shaq’s dimensions from age 6 – 25. If choosing shoe size, note that the shoe size at age 4 is in Child Size. Age Height Weight (pounds) Shoe Size 4 3'10.5" 56 pounds Size 12 Y 6 4'3.5" 82 pounds Size 2 8 4'8.75" 108 pounds Size 4 10 5'3.25" 139 pounds Size 7.5 12 5'10" 192 pounds Size 10.5 16 6'7" 265 pounds Size 15 21 7'1" 302 pounds Size 20 25 7'1" (216 cm) 310 pounds Size 22 Figure. _________________________________________________ Data Analysis: Biology 101 Lab Data Tables and Graphs – 9  Puzzle: Data Graphs Terms: Dependent, Dependent, Horizontal, Independent, Independent, Label, Legend, Line, Linear, Logarithmic, Mean, Median, Mode, Percentage, Pie, Positive, Range, Relationship, Scatterplot, Title Across Down 1. axis of a line graph that contains the “Time periods” 2. a scatterplot is used to determine the ___ between two 4. a graph in the form of a circle is called a ___ chart different things 6. short explanation of what is in the graph, written at top 3. Pie charts usually show the data as a __ of the whole 10. each axis must have a ___ or explanation of that 5. the variable that is not changed by other variables variable 7. scale of the graph axis numbered 1, 10, 100, 1000, etc. 12. the variable that depends on other factors and can 8. the data value that is repeated most frequently change 9. the middle data value 13. if the trend line in a scatterplot rises to the right, then 10. explanation of what each graph line (or bar, sector) this show a __ relationship between the two variables represents 14. average of all data points 11. difference between the smallest and largest data 15. type of graph usually used to show how something values changes over time 15. scale of the graph axis numbered 1,2,3,4,5, etc 16. graph sometimes called an X-Y plot Biology 101 Lab Data Tables and Graphs – 10