NAME
Lab Day
LABORATORY 1
DATA EXPRESSION AND
ANALYSIS
OBJECTIVES
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•
•
•
•
•
•
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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.
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.
Table 1-1 Exponents
Common Number
•
Exponential Number
4000
=
4.0 times 1000
=
4.0 x 10 3
750,000
=
7.5 times 100,000
=
7.5 x 10 5
0.0003
=
3.0 times 1/10,000
=
3.0 x 10 -4
0.0000864
=
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
570,000
3,630,000
0.00003
0.0000056
0.0000000044
•
Arrange the following numbers from the smallest to the largest by using their
letters.
A
B
C
D
E
F
2.3 x 10 -3
1.8 x 10 - 5
5.0 x 10 4
4.6 x 10 4
2.0 x 10 7
2.0 x 10 -2
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 kilowhich 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 microunits 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 1000. 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
1/1,000,000
kilo
k
1.0 x 10 6
1.0 x 10 3
deci
d
10
centi
c
1.0 x 10 -1
1.0 x 10 -2
milli
m
micro
µ (mu)
nano
n
pico
p
1/1000
100
1.0 x 10 -3
1.0 x 10 -6
1.0 x 10 -9
1.0 x 10 -12
1000
1,000,000
1,000,000,000
1,000,000,000,000
Large
M
Small
k
s
d
c
m
µ
Figure 1-1 Metric Prefix Size Comparison(see Table 1-3 for symbols. s = standard unit)
n
p
Length
The standard unit of length is the meter (m) and is equivalent to 39.37 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 28.35 grams per ounce.
One
gram
1000
mg
1,000,000
µg
Figure 1-3 Mass Relationships from Grams to Nanogram
1.0 x 109
ng
1.0 ng 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 cm3) and a microliter is
equivalent to a cubic millimeter (mm3). These terms are sometimes used in the medical
profession.
1 liter = 1000 ml = 1,000,000 µl
Figure 1-4 Liter Diagram
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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)?
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
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
1995 Averages
15.70%
15.70%
12.60%
17.00%
13.90%
10.70%
11.80%
15.20%
14.30%
13.80%
10.60%
14.10%
15.30%
18.30%
16.20%
13.50%
16.60%
17.00%
14.30%
15.00%
2010 Averages Percent increase - 1995 to 2010
32.30%
105.73%
25.90%
64.97%
25.40%
101.59%
30.60%
80.00%
24.80%
78.42%
19.80%
85.05%
21.80%
84.75%
28.00%
84.21%
26.10%
82.52%
28.70%
107.97%
25.70%
142.45%
25.70%
82.27%
27.70%
81.05%
29.10%
59.02%
28.10%
73.46%
29.00%
114.81%
31.50%
89.76%
31.60%
85.88%
26.50%
85.31%
27.10%
80.67%
State
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
State Averages
1995 Averages
11.60%
17.20%
14.60%
19.40%
16.90%
13.00%
15.20%
13.10%
12.90%
12.30%
11.60%
14.30%
16.30%
15.20%
16.10%
12.90%
13.60%
16.20%
12.80%
16.60%
14.50%
16.40%
16.00%
12.00%
13.40%
14.20%
13.90%
17.70%
16.40%
14.00%
14.64%
2010 Averages Percent increase - 1995 to 2010
22.30%
92.24%
30.50%
77.33%
25.30%
73.29%
34.40%
77.32%
30.30%
79.29%
23.80%
83.08%
27.60%
81.58%
25.00%
90.84%
25.60%
98.45%
24.10%
95.93%
25.60%
120.69%
24.70%
72.73%
29.40%
80.37%
28.00%
84.21%
29.60%
83.85%
31.40%
143.41%
25.40%
86.76%
28.50%
75.93%
24.30%
89.84%
30.90%
86.14%
28.70%
97.93%
31.90%
94.51%
30.10%
88.13%
23.40%
95.00%
23.50%
75.37%
25.90%
82.39%
26.40%
89.93%
32.20%
81.92%
27.40%
67.07%
25.40%
81.43%
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?
13.
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?
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 yaxis). Graphs can be line, histograms (bars), pie charts or scatter in form. See Figures 1-6
through 1-10.
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.
Table 1-5 Age and Weight in Boys
Age (years)
Weight (kilograms)
Age (years)
Weight (kilograms)
0
1
2
3
4
5
6
7
8
9
3.4
10.1
12.6
14.6
16.5
18.9
21.9
24.5
27.3
29.9
10
11
12
13
14
15
16
17
18
32.6
35.2
38.3
42.2
48.8
54.5
58.8
61.8
63.1
19.
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.
70
60
weight (kilograms)
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
age (years)
Figure 1-6 Line Graph of the Body Weight Data
70
60
weight (kilograms)
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18
age (years)
Figure 1-7 Bar Chart of the Body Weight Data
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.
Age Distribution 8% 24% < 20 20-­‐24 30% 25-­‐39 40 + 38% Figure 1-8 Age Distribution at Mesa College (2015)
(Data from SDCCD)
23.
Which age group has the highest percentage?
24.
Which age group makes up 24% of the student population?
25.
What percentage group do you belong to?
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 1-10.
30000 25000 20000 15000 Number Accepted 10000 Number Not Accepted 5000 0 Figure 1-9 Student Applicants to California Nursing Schools
(Clustered column or bar graph)
Data from California Board of Registered Nursing
45000 40000 35000 30000 25000 20000 15000 10000 Number Not Accepted Number Accepted 5000 0 Figure 1-10 Student Applicants to California Nursing Schools
(Stacked column or bar graph)
Data from California Board of Registered Nursing
26.
Compare the trend in the number of applicants applying to nursing schools in
California from 2000/2001 to 2009/2010.
27.
Compare the trend in the number of applicants accepted to nursing schools in
California from 2000/2001 to 2009/2010.
28.
How does the percent of accepted applicants change through the years?
GRAPHING DATA
OXYGEN AND HEMOGLOBIN
Table 1-6 Relationship between Oxygen Levels and Percent Saturation
Partial Pressure
(Concentration) of
O2 (mmHg)
0
10
20
30
40
50
60
70
80
90
100
Percent O2
Saturation on
Hemoglobin
0
14
35
60
75
84
89
92
95
96
97
29.
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 1-11. Draw straight lines connecting datum point to
datum point.
100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Figure 1-11 Hemoglobin Saturation verses Oxygen Levels
90 100 31.
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.
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•
•
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 1-12.
Calculate the averages for the entire class, male students, and female students and
place on Table 1-8.
Table 1-7 Class Data (raw) for Student Height (inches)
Height
(inches)
Number of
Females
Number of Height
Males
(inches)
58
69
59
70
60
71
61
72
62
73
63
74
64
75
65
76
66
77
67
78
Number of
Females
Number of
Males
68
8 Number of Students 7 6 5 4 3 2 1 0 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Height (inches) Figure 1-12 Student Height (inches) - Plot as a stacked bar graph
(See Figure 1-10 for an example)
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.