20.4 Scatter and Line Graphs

• Spreadsheet for 20.4

Activity 20.4.1 – Displaying data as a scatter (x-y) plot

Perhaps the most common format for plotting experimental data is the scatter plot (x-y plot) that can show a relationship between two variables (figure 20.11B).  The independent variable is placed on the x-axis, and the dependent variable on the y-axis.  The independent variable must represent a continuum, such as temperature, time, or light intensity, rather than discrete points or factors such as blood type,  habitat, or wing design.  For example, there is a continuum between any two times (e.g. one can divide the time between 5.0 and 5.2 seconds ad infinitum… 5.1 seconds, 5.11, 5.111, etc.), but not between blood types (you have either A, B, AB or O, but nothing in between). Figure 20.11B[i] is a scatter (x-y) plot of atmospheric ozone concentration in the Los Angeles basin as a function of time for a smoggy day in September 2006.  Although the measurements were made at one-hour intervals, they could have been made at any time in between because time is a continuous variable.  When the data points are plotted, one can see a relationship between time and ozone concentration.  The atmospheric ozone concentration varies throughout the day, regardless of location.  It is highest in the early afternoon and lowest at night. 

(1) Air pollution trends:  Figure 20.11B demonstrates changes in ozone concentration in a 24-hour period in the mountains and valleys of Los Angeles for a given day in September.  Compare this data with that from the same day at the beach by plotting the data from the "beach" column.  Does ozone pollution at the beach show the same daily fluctuations?  Where is ozone pollution the worst?

(2) Air pollution trends in your region. Access the Environmental Protection Agency [epa.gov] website or you local air quality management district website and obtain the values for ozone or other air pollutants for a given day in the closest large city. Record the time in one column and the pollution concentration in the adjacent column.  It is not necessary to have data at even time intervals since time is a continuous variable.  Plot data such that time is on the x-axis (independent variable) and pollution concentration is on the y-axis.  Adjust the y-axis scale so daily variations can be clearly seen.  Plot data for three days on three separate plots and summarize the trends. 

(3) Body size and brain size:  Scientific researchers are always searching for correlations between variables in an attempt to better understand the world around us.  Such studies have lead to many important discoveries, such as the link between smoking and lung cancer, or the link between alcohol consumption and fetal alcohol syndrome.  Figure 20.12A reports data for average body weight and brain size for a variety of animals.  Plot this data such that body weight is on the x-axis and brain weight is on the y-axis.  Does there appear to be a relationship between body weight and brain size?  Add a linear trendline (best fit line) to the chart.  Are humans above or below the trendline? Explain.

(4) Classifying Stars:  Astronomers classify stars according to their temperature and absolute brightness.  A plot of absolute brightness vs. temperature is known as a Hertzprung-Russell diagram and is used to identify stars as main sequence stars, white dwarfs, giants, and super giants.  Figure 20.12B shows the temperature and absolute brightness measures for stars easily seen from earth.  Make a Hertzprung-Russell diagram by creating an X-Y (scatter plot) plot in which temperature is on the x-axis, and absolute brightness is on the y-axis.  Draw a line through the dots that form a trend diagonally across the chart.  These stars are part of the main sequence.  Is the Sun a main sequence star?

(5) Sunspots: A sunspot is a relatively cool region of the photosphere (Sun’s surface) that is characterized by intense magnetic activity.  Figure 20.12C[ii] records some the major sunspots by year from 1970 to 1999. Plot the number of sunspots as a function of time on an x-y (scatter plot). Describe the pattern you see.

Activity 20.4.2 Displaying Data with Line Graphs

A line graph is similar to an X-Y plot, except that the independent variable is discrete and evenly spaced.  For example, figure 20.13 shows the relationship of atomic radius to atomic number.  The atomic radius is one of the most important properties of an atom and influences a number of other properties such as boiling point, melting point, and reactivity.  Atomic radius is a continuous variable, but atomic number is a discrete, evenly spaced variable. Atomic number represents the quantity of protons in the nucleus of an atom and therefore can only be represented by whole numbers. There can be two or three protons in a nucleus, but not 2.2 or 2.356. 

Chemistry

(1) Is boiling point a periodic property?  The periodic table of the elements derives its name from the fact that many properties are periodic, or repeating.  Members of a family (column) share similar characteristics, so when a property is plotted as a function of atomic number, one notices repeating patterns.  Notice that atomic radius is periodic (figure 20.13B), with relatively high radii in the first family (elements 3, 11, and 19) and small radii in the Noble gasses (elements 2, 8, 18). Create a line graph of boiling point vs. atomic number for the first 20 elements using the data provided in figure 20.13A.  Is boiling point a periodic property?  Which families have the highest and lowest boiling points?

(2) Is melting point a periodic property? Create a line graph of melting point vs. atomic number for the first 20 elements using the data provided in figure 20.13A.  Is melting point a periodic property?  Which families have the highest and lowest melting points?

(3) Is atomic mass a periodic property? Create a line graph of atomic mass vs. atomic number for the first 20 elements using the data provided in figure 20.13A.  Is atomic weight a periodic property?

(4) Is first ionization energy a periodic property?  First ionization energy is the energy required to remove the first electron from an atom, and is a measure of how reactive an element is. Elements with extremely high ionization energies will not ionize to form ionic bonds. Create a line graph of first ionization energy for the first 20 elements using the data provided in figure 20.13A. Is first ionization energy periodic? Which families have the highest and lowest ionization energies?

(5) Is electron affinity a periodic property?  Create a line graph of electron affinity for the first 20 elements using the data provided in figure 20.13A.  Is electron affinity a periodic property?  Which families have the highest and lowest electron affinities?

Biology

(6) How did life expectancy change during the last century? Life expectancy is defined as the average number of years that a person can be expected to live.  Figure 20.14A[iii] shows the average life expectancy for Americans born on the years specified.  Create a line graph of life expectancy as a function of birth year and summarize your findings. List the factors that you believe have influenced the trends you see.

(7) What are the trends in the causes of death? The twentieth century was marked by dramatic improvements in medicine as reflected in the increase in life expectancy (figure 20.14A).  Are people still dying of the same diseases?  Create a line graph of death rate (deaths per 100,000 population) for tuberculosis, cancer, and cardiovascular disease (heart attacks, etc.).  Explain the trends you see.

(8) Rare and endangered species: In an effort to preserve biodiversity, the United States Wildlife service lists species that are threatened or endangered with extinction.  Figure 20.14B shows the number of species that have received this designation between 1980 and 2000.  Figure 20.14C[iv] plots the trends for mammals, birds, and amphibians.  Plot the values for reptiles, fish, and plants on a similar graph and summarize your findings.