Graphing Information- Integrated Science (ISCI 2001/2002)
There will be a few key elements to any graph.
Data Range
The graph is a graphical interpretation of some data. Generally, you will create a spreadsheet that generates some type of data, and use the graph to illustrate the data. When you define a graph, you will need some way to explain which data is being depicted. You can usually select the data you want with a range.
X and Y axes
As you may remember, the X axis is the stuff that goes along the horizontal border of the chart. The Y axis is the vertical stuff. Most spreadsheet programs try to guess which stuff you want plotted as the X axis and which you want as the Y axis. If the graph looks completely wrong, you might want to look for some kind of feature that allows you to change the X - Y orientation.
Upper and Lower Bounds
You might want to specify the upper and lower limits of the axes. The program will usually try to guess what you want, but you may still need to modify it.
Labels
There will usually be an option for setting or changing the labels on a graph. This will allow you to put informative (or misleading, I guess) labels on the graph to make it easier to read. (unless you are sneaky.)
Graph type
You will usually get some type of option to change the type of graph that is displayed. See below for more information about graph types.
Types of Graphs
There are a number of major styles you can choose from when creating a graph. The style you choose implies some things to your readers.
Bar Graphs
Bar graphs compare distinct items or show single items at distinct intervals. Usually, a bar chart is laid out with categories along the vertical axis and values along the horizontal axis. In other words, the bars are horizontally placed on the page. Bar charts are useful for comparing data items that are in competition, so it makes sense to place so it makes sense to place the longest bars on top and the others in descending order beneath the longest one.
Line Graphs
A line graph plots the value of the variable as a specific point, then 'connects the dots' in order to give you some idea of the relationship of consecutive points.
Line charts may also be used to show how the value of a variable changes over time. Unlike bar and column charts, line charts imply continuous change rather than a number of discrete points. For this reason, line charts are better at implying a trend. For example, if you are doing an experiment about the number of fish in a certain pond, you might be interested in the number of fish in the pond at a certain time, but you may also be very concerned with the trend of the fish population. Is it increasing or decreasing?
Just because a line chart implies trends does not necessarily mean they are there! Be careful when interpreting such charts that you do not automatically assume intermediate values by the line placement.
Pie Charts
A pie chart is used to show proportions of a whole. It is very useful for figures that relate to a larger sum, such as demographic data or budget information. It is easy to get a feel for the relationship between component values when they are placed in a pie chart. Be careful that you do not have too many slices in the pie, or they will become meaningless.
Also, note that a pie chart is usually used as a snapshot of ONE moment in time. If you want to show relationships as part of a whole over time, you would use an area chart. If you want to look at a number of pie charts at once, you might consider a doughnut chart. (look it up in online help or just play around with it!)
Scatter Plot
A scatter plot is the simplest type of graph. It simply plots the data points against their values, without adding an connecting lines, bars or other stuff. This is visually the least appealing type of graph, but the lack of bells and whistles can actually be an advantage. Since all the other types of graphs tend to have some kind of psychological implication built in (eg bar charts imply comparison, line graphs imply continuity), scatter diagrams are devoid of this type of clutter. If you are searching for the patterns and meaning in a graph, you may find the scatter diagram the clearest representation of the data. Once you understand what it means, you can use one of the other types of graph to give your readers whichever impression you choose.
LINE GRAPH VS. BAR GRAPH OR PIE GRAPH?
If the presentation is to highlight various data as a percent of the total data, then a pie graph is ideal. Pie graphs might be used for example to demonstrate the composition of the white cell differential count. They are the most often used graph type for business use, particularly in displaying budget details.
Pie Graphs are circular presentations which are drawn by summing your data and computing the percent of the total for each data entry. These percent values are then converted to portions of a circle (by multiplying the percent by 360 ° ) and drawing the appropriate arc of a circle to represent the percent. By connecting the arc to the center point of the circle, the pie is divided into wedges, the size of which demonstrate the relative size of the data to the total. If one or more wedges are to be highlighted, that wedge can be drawn slightly out of the perimeter of the circle for what is referred to as an exploded view.
More typical of data presented in cell biology, however, are the line graph and the bar graph. There is no hard and fast rule for choosing between these graph types, except where the data is non-continous. Then, a bar graph must be used. In general, line graphs are used to demonstrate data which is related on a continous scale, whereas bar graphs are used to demonstrate discontinous or interval data.
Suppose, for example, that you decide to count the number of T-lymphocytes in four slices of tissue, one each from the thymus, Payer's patches, a lymph node and a healing wound on the skin. Let's label each of these as T, P, L and S respectively. The numbers obtained per cubic centimeter of each tissue are T=200, P=150, L=100 and S=50. Note that there is a rather nice linear decrease in the numbers if T is placed on the left of an x axis, and S to the right. A linear graph of this data would give a nice straight line, with a statistical regression fit and slope. But look at the data! There is no reason to place T (or P,L or S) to the right or left of any other point on the graph - the placement is totally arbitrary. A line graph for this data would be completely misleading since it would imply that there is a linear decrease from the thymus to a skin injury AND that there was some sort of quantitative relationship among the tissues. There is certainly a decrease, and a bar graph could demonstrate that fact, by arranging the tissue type on the x axis in such a way to demonstrate that relationship - but there is no inherent quantitative relationship between the tissue types which would force one and only one graphic display. Certainly, the thymus is not four times some value of skin (although the numbers are).!
However, were you to plot the number of lymphocytes with increasing distance from the point of a wound in the skin, an entirely different presentation would be called for. Distance is a continous variable. We may choose to collect the data in 1 mm intervals, or 1 cm. The range is continous from 0 to the limit of our measurements. That is we may wish to measure the value at 1 mm, or 1.2 mm or 1.23 mm or 1.23445 mm. The important point is that the 2 mm position is 2x the point at 1 mm. There is a linear relationship between the values to be placed on the x axis. Therefore a linear graph would be appropriate, with the dots connected by a single line. If we choose to ignore the 1.2 and 1.23 and round these down to a value of 1, then a bar graph would be more appropriate. This latter technique (dividing the data in appropriate intervals and plotting as a bar graph) is known as a Histogram. This graph is very familiar to students since it is the graph used for the display of grade distributions.
Having decided that the data has been collected as a continous series, and that the data will be plotted on a linear graph, there are still decisions to be made. Should the data be placed on the graph as individual points with no lines connecting them (a Scattergram)? Should a line be drawn between the points (known as a Dot-to-Dot)? Should the points be plotted, but curve smoothing be applied? If the latter, what type of smoothing?
If the data collected involves two or more sets of data having a common x axis, but varying y axes (or values), then a multiple graph may be used. The rules for graphing apply to each set of data, with the following provision; Keep the number of data sets on any single graph to an absolute minimum. It is far better to have three graphs, each with 3 lines (or bars) than to have a single graph with 9 lines. A graph that contains an excess of information (such as 9 lines) is usually ignored by the viewer (as are tables with extensive lists of data). For this same reason, all unnecessary clutter should be removed from the graph; e.g. grid marks on the graph are rarely useful.
Finally, it is possible to plot two variables, y and z, against a common value, x. This is done with a 3D graphic program. The rules for designing a graph follow for this type of graph, and the use of these should clearly be left to computer graphics program. These graphs often look appealing with their hills and valleys, but rarely impart any more information than two separate 2D graphs. Perhaps the main reason is that people are familiar with two dimensional graphics, but have a more difficult time visually interpreting three dimensional graphs.
Graphing Data
The volume of a gas decreases as the temperature of the gas decreases. A sample of gas was collected at 100 degrees Celsius and then cooled. The changes in the volume of the sample are shown below.
T ( oC ) / V ( ml )100 / 317
80 / 297
60 / 288
40 / 278
30 / 252
20 / 243
10 / 236
0 / 233
-10 / 227
-30 / 202
- Construct a line graph using the data. Which is the dependent and independent variable?
- Construct another graph that will allow you to extrapolate (extend the graph beyond measured data) the graph to reach a gas volume of 0 ml. The temperature at which the volume of the gas reaches zero is the theoretical temperature of Absolute Zero. From this graph, what is the Celsius Temperature for Absolute Zero?
Practice Interpreting Data:
In addition to drawing graphs, it is also important that you be able to intrepret data that is represented in graph form. The following examples are provided to help you develop the ability to read information shown on a graph.
- Identify the graph that matches each of the following stories:
- I had just left home when I realized I had forgotten my books so I went back to pick them up.
- Things went fine until I had a flat tire.
- I started out calmly, but sped up when I realized I was going to be late.
- The graph at the right represents the typical day of a teenager. Answer these questions:
- What percent of the day is spent watching TV?
- How many hours are spent sleeping?
- What activity takes up the least amount of time?
- What activity takes up a quarter of the day?
- What two activities take up 50% of the day?
- What two activities take up 25% of the day?
- Answer these questions about the graph at the right:
- How many sets of data are represented?
- On approximately what calendar date does the graph begin?
- In what month does the graph reach its highest point?
- Answer these questions about the graph on the right:
- How many total miles did the car travel?
- What was the average speed of the car for the trip?
- Describe the motion of the car between hours 5 and 12?
- What direction is represented by line CD?
- How many miles were traveled in the first two hours of the trip?
- Which line represents the fastest speed?
- Answer these questions about the graph at the right:
- What is the dependent variable on this graph?
- Does the price per bushel always increase with demand?
- What is the demand when the price is 5$ per bushel?
- The bar graph at right represents the declared majors of freshman enrolling at a university. Answer the following questions:
- What is the total freshman enrollment of the college?
- What percent of the students are majoring in physics?
- How many students are majoring in economics?
- How many more students major in poly sci than in psych?
- This graph represents the number of A's earned in a particular college algebra class. Answer the following questions:
- How many A's were earned during the fall and spring of 1990?
- How many more A's were earned in the fall of 1991 than in the spring of 1991?
- In which year were the most A's earned?
- In which semester were the most A's earned?
- In which semester and year were the fewest A's earned?
- Answer these questions about the graph at the right:
- How much rain fell in Mar of 1989?
- How much more rain fell in Feb of 1990 than in Feb of 1989?
- Which year had the most rainfall?
- What is the wettest month on the graph?
9. Answer these questions about the data table:
- What is the independent variable on this table?
- What is the dependent variable on this table?
- How many elements are represented on the table?
- Which element has the highest ionization energy?
- Describe the shape of the line graph that this data would produce?
(volts)
2 / 24.46
4 / 9.28
6 / 11.22
8 / 13.55
10 / 21.47
10. Answer the following using the data table:
- How many planets are represented?
- How many moons are represented?
- Which moon has the largest mass?
- Which planet has a radius closest to that of Earth?
- How many moons are larger than the planet Pluto?
- Which of Jupiter's moons orbits closest to the planet?
- Which planet is closest to Earth?
Distance Radius Mass
Name Orbits (000 km) (km) (kg)
------
Sun 697000 1.99 x 1030
Jupiter Sun 778000 71492 1.90 x 1027
Saturn Sun 1429000 60268 5.69 x 1026
Uranus Sun 2870990 25559 8.69 x 1025
Neptune Sun 4504300 24764 1.02 x 1026
Earth Sun 149600 6378 5.98 x 1024
Venus Sun 108200 6052 4.87 x 1024
Mars Sun 227940 3398 6.42 x 1023
Ganymede Jupiter 1070 2631 1.48 x 1023
Titan Saturn 1222 2575 1.35 x 1023
Mercury Sun 57910 2439 3.30 x 1023
Callisto Jupiter 1883 2400 1.08 x 1023
Io Jupiter 422 1815 8.93 x 1022
Moon Earth 384 1738 7.35 x 1022
Europa Jupiter 671 1569 4.80 x 1022
Triton Neptune 355 1353 2.14 x 1022
Pluto Sun 5913520 1160 1.32 x 1022