# DATA EXPRESSION AND ANALYSIS

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1 NAME Lab Day DATA EXPRESSION AND ANALYSIS LABORATORY 1 OBJECTIVES Understand the basis of science and the scientific method. Understand exponents and the metric system. Understand the metric units of length, weight, and volume. Perform metric conversions. Explain the differences between direct and inverse relationships between variables. Identify the different graphical ways of viewing data. Analyze numerical and graphical data. Collect and graph data.

2 2 SCIENCE Science is the pursuit of gaining knowledge or the process of developing and organizing knowledge in the form of testable explanations of the world and universe. Scientific inquiry involves the principles laid down in the scientific method. Scientists propose a hypothesis as an explanation for the area of investigation, and then design an experiment. The results of the experiment must be repeatable and subject to peer review. The scientific method insures full disclosure by the experimenters so that other scientists can reproduce and verify the results. These aspects of the scientific method reduce errors in setting up the experimental design and in reducing the bias of the investigator. Outside the scientific process are belief systems that include philosophies, religions, ideologies, and pseudoscience. Specific examples of pseudoscience include psychic powers, homeopathy, and the effect of the full moon on human behavior. INTRODUCTION The scientific community utilizes a common basis for measuring, calculating, and expressing numerical values and experimental data. This laboratory exercise explores the use of scientific notation and the treatment and analysis of data. SCIENTIFIC NOTATION EXPONENTS Most numbers we encounter on a daily basis can be written as whole numbers or as fractions. This method is convenient for small values but can become cumbersome for large numbers and very small fractions. Expressing a number exponentially can simplify and help differentiate awkward numbers. The process of changing a number to its exponential value is to have a single digit to the left of the decimal point with fractions and exponents to the right of the decimal point as shown on Table 1-1. Exponents can be either positive for numbers greater than one or negative for numbers less than one. A higher exponent value represents a larger number while a more negative exponent value represents a smaller number.

3 3 Table 1-1 Exponents Common Number Exponential Number 4000 = 4.0 times 1000 = 4.0 x ,000 = 7.5 times 100,000 = 7.5 x = 3.0 times 1/10,000 = 3.0 x = 8.64 times 1/100,000 = 8.64 x 10-5 Convert the numbers on the left on Table 1-2 to exponential numbers on the right of Table 1-2. Table 1-2 Exponent Calculations Number Exponential Number 60, ,000 3,630, Arrange the following numbers from the smallest to the largest by using their letters. A 2.3 x 10-3 B 1.8 x 10-5 C 5.0 x 10 4 D 4.6 x 10 4 E 2.0 x 10 7 F 2.0 x 10-2

4 4 METRIC SYSTEM Scientists, clinicians and most countries utilize the metric system as a standardizing system for measuring the physical and biological world around them. The metric system is based upon powers of ten where units of measurement increase or decrease by tens, hundreds or thousands, etc. The standard unit of length is the meter (m), mass (weight) the gram (g or gm), and volume the liter (l or L). Various prefixes are used with the metric system to represent units of measurement larger or smaller than the standard unit and are applicable to length, mass and volume. The most common prefix for values larger than the standard unit is kilo- which represents a thousand standard units and the mega- that is one million standard units. The more common prefixes used in biology which represent fractions of the standard unit are deci-, centi-, milli-, micro-, nano-, and pico- as shown on Table 1-3 and Figure 1-1. There are one thousand nano- units in a micro- unit and one thousand micro- units in a milli- unit. One thousand milli- units are in the standard unit of measurement. Thus 1000 times 1000 equal one million nano- units for each milli- unit. There are one billion nano- units per standard unit, 1000 times 1000 times There are also one trillion pico- units per standard unit of measurement. Table 1-3 Metric System Prefixes Prefix Symbol Value Compared to the Standard Unit Number of units in the Standard Unit mega M 1.0 x /1,000,000 kilo k 1.0 x /1000 deci d 1.0 x centi c 1.0 x milli m 1.0 x micro µ (mu) 1.0 x ,000,000 nano n 1.0 x ,000,000,000 pico p 1.0 x ,000,000,000,000 Large Small M k s d c m µ n p Figure 1-1 Metric Prefix Size Comparison- (see Table 1-3 for symbols. s = standard unit)

5 5 Length The standard unit of length is the meter (m) and is equivalent to inches or just over one yard. The common metric lengths used in biology include the decimeter (one tenth of a meter), centimeter (one hundredth of a meter), the millimeter (one thousandth of a meter) and the micrometer (one millionth of a meter) as shown on Figure 1-2. Most human cells range from 50 to 200 micrometers in diameter. 1/10 m = 1 dm = 10 cm = 100 mm = 100,000 µm Figure 1-2 Length Relationships from Meters to Micrometers Mass or Weight The standard unit of mass is the gram (g) (the amount of artificial sweetener in packages found in family restaurants). The common weights seen in biology range from large kilogram organisms to small nanograms of chemicals located within the body's fluid. See Figure 1-3. There are roughly 2.2 pounds per kilogram and 454 grams per pound. There are grams per ounce. One gram 1000 mg 1,000,000 µg 1.0 x 10 9 ng 1.0 ng Figure 1-3 Mass Relationships from Grams to Nanogram

6 6 Volume The standard unit of volume is the liter (l or L) and is equivalent to 1.06 quarts. Volume in the metric system can be expressed in liters or in cubic measurements of length. The common units used in physiology are the milliliter (one thousandth of a liter) and the microliter (one millionth of a liter) as shown on Figure 1-4. One milliliter is also equal to a cubic centimeter (cc or cm 3 ) and a microliter is equivalent to a cubic millimeter (mm 3 ). These terms are sometimes used in the medical profession. 1 liter = 1000 ml = 1,000,000 µl Figure 1-4 Liter Diagram

7 7 Review the material on Table 1-3, Figure 1-1, Figure 1-2, Figure 1-3, and Figure 1-4 and then calculate the following conversions. Note: the smaller the unit the more there are of them in a given length, weight, and volume. Example: convert 500 grams to kilograms. (500 grams/1) times (1 kilogram/1000 grams) = 500/1000 = 0.5 kg 1. How many milliliters are in one liter? 2. How many microliters are in one milliliter? 3. How many nanograms are in 5 milligrams? 4. How many microliters are in 45 liters? 5. How many grams are in 4.2 kilograms? 6. How many milligrams are in 69,000 micrograms? 7. How many millimeters are in 50 centimeters? 8. How many kilometers are in 65,400 meters? 9. How many milliliters are in 200 cubic centimeters (cc)?

8 8 DATA ANALYSIS The data obtained from scientific research or laboratory exercises can be more readily interpreted when presented in a table, graph, or chart. Tabular values are usually presented on tables as raw data, or treated data. 10. Define average or mean TABLES Information can be obtained by examining data as found on a table. Below is a table showing data about obesity in the United States. Obesity is generally defined as having a body mass index (BMI) of 30 or greater. BMI can be calculated by multiplying your weight in pounds by 703 and then dividing by your height in inches times your height in inches. Formula = Weight (lbs.) * 703 / [height (in)] 2 Table 1-4 Obesity Percentages by States (Data is from Behavior Risk Factor Surveillance System & CDC, 2011) State 1995 Averages 2010 Averages Percent increase to 2010 Alabama 15.70% 32.30% % Alaska 15.70% 25.90% 64.97% Arizona 12.60% 25.40% % Arkansas 17.00% 30.60% 80.00% California 13.90% 24.80% 78.42% Colorado 10.70% 19.80% 85.05% Connecticut 11.80% 21.80% 84.75% Delaware 15.20% 28.00% 84.21% Florida 14.30% 26.10% 82.52% Georgia 13.80% 28.70% % Hawaii 10.60% 25.70% % Idaho 14.10% 25.70% 82.27% Illinois 15.30% 27.70% 81.05% Indiana 18.30% 29.10% 59.02% Iowa 16.20% 28.10% 73.46% Kansas 13.50% 29.00% % Kentucky 16.60% 31.50% 89.76% Louisiana 17.00% 31.60% 85.88% Maine 14.30% 26.50% 85.31% Maryland 15.00% 27.10% 80.67%

9 9 State 1995 Averages 2010 Averages Percent increase to 2010 Massachusetts 11.60% 22.30% 92.24% Michigan 17.20% 30.50% 77.33% Minnesota 14.60% 25.30% 73.29% Mississippi 19.40% 34.40% 77.32% Missouri 16.90% 30.30% 79.29% Montana 13.00% 23.80% 83.08% Nebraska 15.20% 27.60% 81.58% Nevada 13.10% 25.00% 90.84% New Hampshire 12.90% 25.60% 98.45% New Jersey 12.30% 24.10% 95.93% New Mexico 11.60% 25.60% % New York 14.30% 24.70% 72.73% North Carolina 16.30% 29.40% 80.37% North Dakota 15.20% 28.00% 84.21% Ohio 16.10% 29.60% 83.85% Oklahoma 12.90% 31.40% % Oregon 13.60% 25.40% 86.76% Pennsylvania 16.20% 28.50% 75.93% Rhode Island 12.80% 24.30% 89.84% South Carolina 16.60% 30.90% 86.14% South Dakota 14.50% 28.70% 97.93% Tennessee 16.40% 31.90% 94.51% Texas 16.00% 30.10% 88.13% Utah 12.00% 23.40% 95.00% Vermont 13.40% 23.50% 75.37% Virginia 14.20% 25.90% 82.39% Washington 13.90% 26.40% 89.93% West Virginia 17.70% 32.20% 81.92% Wisconsin 16.40% 27.40% 67.07% Wyoming 14.00% 25.40% 81.43% State Averages 14.64% 27.34% 86.75% 11. What is the percentage of obesity in California in the year 2010 as seen from the data on Table 1-4? 12. Is the level of obesity in California above or below the average of the other states?

10 Which state has the lowest percentage of obesity in 2010 and what is the value? 14. Which state has the highest percentage of obesity in 2010 and what is the value? 15. Which state has the lowest percentage of increase from 1995 to 2010? 16. Which two states have the highest percentage of increase from 1995 to 2010? 17. What can be said about obesity in the United States from 1995 to 2010?, 18. What are your thoughts about what might be causing this epidemic in the United States?

11 11 GRAPHS Graphical representation of the data allows for a quick pictorial analysis of the information. A graph usually has two variables observed in the experiment with one plotted along the horizontal x-axis and the other variable along the vertical y-axis. The relationship between the variables of a graph can be linear or curvilinear. The relationship can also show a positive or direct relationship, a negative or inverse relationship, or a neutral relationship where the dependent variable is constant. See Figure 1-5. A B C D E Figure 1-5 Relationships between the variables of a graph Graphs A, B and C are linear graphs with a graph A having a positive or direct relationship, graph B a negative or inverse relationship, and graph C as being constant. Graph D shows a positive curvilinear relationship and E a negative or inverse curvilinear relationship. The independent variable is usually divided by regular intervals, in order to observe its effect on the dependent variable. Most graphs plot the independent variable on the abscissa (horizontal x-axis) and the dependent variable on the ordinate (vertical y-axis). Graphs can be line, histograms (bars), pie charts or scatter in form. See Figures 1-6 through A graph is first constructed by differentiating between the dependent and independent variables, and their axes. The spacing of the tabular data on the axes is important. This is achieved by spreading the values out along the axes and by using the same distances for equivalent values. The first datum point is then ready for plotting on the graph. The values for both variables are located on their respective axes. Each value is then moved either vertically or horizontally until both of them intersect for the datum point. This process is then continued for all values. Finally all the data points on the graph are connected point to point with straight ruler drawn lines.

12 12 Table 1-5 Age and Weight in Boys Age (years) Weight (kilograms) Age (years) Weight (kilograms) Which factor (age or weight) on Table 1-5 is the independent variable? 20. Which axis of a graph is the independent variable usually plotted on? 21. What is the relationship between age and body weight as seen on Figure 1-6 and Figure 1-7? 22. What ages show a dramatic increase in growth (slope) in body weight on Figure 1-6 and Figure 1-7? Note: please look at the entire graph for two areas.

13 weight (kilograms) age (years) Figure 1-6 Line Graph of the Body Weight Data weight (kilograms) age (years) Figure 1-7 Bar Chart of the Body Weight Data

14 14 PIE CHART Data can also be visualized in a chart such as a bar chart or pie diagram. A pie chart is a circular diagram that is divided into sections that represent a category of data. The total area or all of the data is usually expressed as 100 percent as shown on Figure 1-8. Figure 1-8 Age Distribution at Mesa College (spring 2009) (Data from SDCCD) 23. Which age group has the highest percentage? 24. Which age group makes up 11% of the student population? 25. What percentage group do you belong to?

15 15 BAR GRAPHS Data expressed with bar or column graphs can show the relationship with clustered side by side bars or stacked with one relationship above the other. Review the column or bar graphs as displayed on Figures 1-9 and Number Accepted Number Not Accepted 0 Figure 1-9 Student Applicants to California Nursing Schools (Clustered column or bar graph) Data from California Board of Registered Nursing Number Not Accepted Number Accepted Figure 1-10 Student Applicants to California Nursing Schools (Stacked column or bar graph) Data from California Board of Registered Nursing

16 Compare the trend in the number of applicants applying to nursing schools in California from 2000/2001 to 2009/ Compare the trend in the number of applicants accepted to nursing schools in California from 2000/2001 to 2009/ How does the percent of accepted applicants change through the years?

17 17 GRAPHING DATA OXYGEN AND HEMOGLOBIN Table 1-6 Relationship between Oxygen Levels and Percent Saturation Partial Pressure (Concentration) of O2 (mmhg) Percent O2 Saturation on Hemoglobin Which factor is the independent variable on Table 1-6? 30. Which specific variable on Table 1-6 is plotted on the vertical axis? Label both axes correctly on Figure 1-11, and plot the data, in a line graph, from Table 1-6 on Figure Draw straight lines connecting datum point to datum point Figure 1-11 Hemoglobin Saturation verses Oxygen Levels

18 Describe the entire relationship between the partial pressure of oxygen gas to the percent of oxygen saturation on hemoglobin and how it changes as the concentration of oxygen increases from 0 mm Hg to 100 mm Hg. DATA ACQUISITION This section of the lab exercise explores the collection of data, the plotting of the data, and its analysis. Measure your height in inches and place it on the front board along with your sex (male or female). Collect all the student data and add to Table 1-7. Plot the data for the male and female students as a stacked column bar graph on Figure Calculate the averages for the entire class, male students, and female students and place on Table 1-8.

19 19 Table 1-7 Class Data (raw) for Student Height (inches) Height (inches) Number of Females Number of Males Height (inches) Number of Females Number of Males Number of Students Height (inches) Figure 1-12 Student Height (inches) - Plot as a stacked bar graph (See Figure 1-10 for an example)

20 20 Table 1-8 Height Averages National Health Statistics Reports 2008 Student average Male average Female average U.S. male average U.S. female average 69.4 inches 63.8 inches 32. Compare the height distribution of the female and male students to each other and to the entire class. 33. Discuss some reasons that could cause a difference between the class data from the average heights in the United States as shown on Table 1-8.

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