EX 9: INVESTIGATE: UNITS, MEASUREMENT, & GRAPHING SKILLS

I.     OBJECTIVES:    By the end of the lab, you should be able to:
1.  Make precise, consistent measurements
2.  Understand sources and consequences of different kinds of errors.
3.  Discuss the appropriateness of averages depending on techniques used.
4.  Compare line and bar graphs and use each appropriately.
5.  Reach consensus in the group.

II.     INTRODUCTION:
The American system of measurement is out of step with the scientific community which uses the metric system (S.I.) - now taught in most elementary schools.  So let's get with it.  Begin by completing Table I.

It is important that you are accurate in making measurements.  Facts and data are not the same.  Data are your records of observations, and they are only as good as your measurements.  Poor measurements lead to poor data: which will adversely affect your ability to draw conclusions.

What to do with your measurements / data?  Present it in some logical or systematic way.  One way is to graph it, a pictorial representation of numerical data or information.  Graphing is a powerful tool for presenting data, and visualizing relationships.

TABLE I.      METRIC PREFIXES AND MULTIPLIERS

Prefix	Abbreviation	multiplier	= multiplier
tera	T	10 to the 12 power	?
giga	G	?	1000,000,000 x
mega	M	10 to the  6 power	?
kilo	k	?	1000 x
hecto	h	10 to the 2 power	?
deca	da	?	10 x
deci	d	10 to the -1 power	?
centi	c	?	1/100 = 0.01 x
milli	m	10 to the -3 power	?
micro	u (near enough)	?	1/1000,000 = 0.000,001
nano	n	10 to the -9 power	?
pico	p	?	1/1000,000,000,000
femto	f     you do it! >>>>	?	?
atto	a    you do it!  >>>>	?	?

To use the table for meters, you read: kilo-meter, km = 1000 m; for volume, milli-liter, ml = 0.001 liter.   All units are in powers of ten.  This decreases two things: memorization of different units for different measurements (see the English System listed below), and the amount of things to memorize.

The English system of units includes length, volume, and weight (please insert their abbreviations).

Length units:     1 yard  (     )  = 3 feet.      Each foot (     ) = 12 inches (     ).  1 m = 39.370", 1" = 2.5400 cm
Volume units:    1 gallon (     )  = 4 quarts.  Each quart (     ) = 2 pints (     ).  (not to mention cups etc)
Weight units:     1 pound (     )  = 16 ounces (      ).  In Britain people also use the stone = 14 lb.

SOME METRIC (S.I.) UNITS, OFTEN USED IN BIOLOGY
Length: meter (m)       Area:  square meter (m^2)      Volume: cubic meter & a smaller unit is liter = 1000 cm^3

Time: second (s)  so   Speed = ?_____________________ Acceleration = ?____________________

Mass: kilogram (kg)   so  Density = ?___________________________

Biomass density (ecology):  kg per square meter (kg of ? / m^2 of ?)______________/_______________

Force or weight:   unit is Newton.  Force = mass x acceleration,  so 1 Newton = 1 kg x 1 m x 1 s^-2.  A unit used in animal movement and in other areas of biology.

Pressure = Force per unit area, so Newton x m^-2: because it acts over a small area a stiletto heel exerts a high pressure.  In addition to studies of animal locomotion, pressure is important in blood circulation, and in breathing.

Energy or Work: 1 Joule = 1 Newton meter = 2.3885 x 10^-4 kilocalories.   The energy in food is usually measured in kcalories per serving (check the label).  The sun is the source of most energy, captured by photosynthesis in plants and WHAT other organisms?__________________________________________________________.

Power or Energy consumption = 1 Watt = 1 Joule per second = 2.3885 x 10^-4 kilocalories per second.  The Metabolic Rate of an organism is usually given in kcal per hour per kg body mass, or kg per hr per m^2 body surface
 

III.     PROCEDURE

A.     LENGTH AND VOLUME
To practice using metric measurements, each member (1-4) of your group makes three exact measurements of the length (L), width (W) and height (H) of a rectangular container (e.g. aquarium), using two measuring tools (stick and tape).

Decide exactly where you will make the measurements:

	describe	describe	describe
length
width
height

Measurements

L1

L2

L3

L4

AveL

W1

W2

W3

W4

AveW

H1

H2

H3

H4

AveH

Stick

Tape

Compare tools: 1 meter on stick = on tape (to nearest 0.1 mm!)_________________(put on blackboard)

Volume of your container using the meter stick (& give units) __________________

Volume of your container using the tape (& give units) ______________________

Of all the measuring tools in the room how can you decide which to believe?
 
 

B.    MASS AND WEIGHT
Measure the mass of  ten coins together (e.g. 10 pennies) using two balances.

	Group 1	Group 2	Group 3	Group 4	Group 5
balance 1
balance 2

How much do the coins vary in mass?
 

Do the balances agree?
 

How would you decide which balance to believe?
 

C.    GRAPHING
Nothing that you have done so far seems worthy of graphing because so far you have not related your measurements (dependent variable) to an independent variable.  To draw a line graph you need both a dependent and an independent variable.  Probably the weight of coins declines with age, because they wear.  The age of your coins was used to sort them, so please look and determine.  Share your data, each group: the average mass and date of their pennies:

Average mass (most reliable balance)

1

2

3

4

5

6

Coin date

About organisms: think of five things (dependent variable) that you could measure, and reasonably expect to be related to something else (independent variable), and describe the probable relationship in as much detail as possible:

dependent variable you measure:	is related to independent variable:	& probable relationship is

D.    PI BY GRAPHING    Measure (don't calculate) the circumference and diameter of the circular object on your table.  Use appropriate tools.  The diameter and circumference must correspond.  Share your data.  Make a graph (see below): plot circumference vertical and diameter horizontal.  Draw the line of best fit.  Give the equation relating diameter & circumference____________  Thus determine pi from the graph:____________
 

Object	1	2	3	4	5	6
Diameter
Circumference

E.    MORE WORK: SOME MATHEMATICS
If 300 g of cereal costs $0.60, how much will 1 g of cereal cost?  How much will $0.01 buy?
 
 
 

If 1 cubic centimeter of a certain material has a mass of 14 g, what volume will 1 g occupy?
 
 
 

If 40 ml of a certain material has a mass of 8 g, what will be the mass of 1 ml of the material?
 
 

DRAWING A GRAPH
The type of graph is important ... when is it appropriate to use a line graph?, when does one use a bar graph?

A BAR graph is used when the information to be portrayed is separate, such as the heights of individuals or plants.  This is because one of the axes (the X axis, by consensus) is DISCONTINUOUS.  For example, the bar graph does not tell us that one plant is older or younger than another, although that may well be the case.

A BAR graph shows only separate information; perhaps it will be easier to understand if we state the fact in this way:  The spaces between the bars on a bar graph have no meaning; they are only put in to make the graph neat and easy to read.  It is not legitimate to connect together the points or dots representing the ends of the bars in a bar graph.

On a LINE graph, however, the spaces along the base do have meaning.  On a line graph the spaces along the base and the side represent a scale on which every point has meaning in relation to every other point.  On a line graph, the horizontal scale and the vertical scale are what mathematicians call CONTINUOUS, meaning that each point is related to every other point, and that you can obtain VALID information from the regions between the points.  The fundamental difference between a line graph and a bar graph is that the line graph has two continuous scales; whereas, a bar graph has only one.

Sometimes, as you will see, it requires using good judgment to decide whether to make a line graph or a bar graph to represent our information.  Now let’s take a quick look at each of the various features absolutely required by every graph:

A)      A GOOD TITLE:
A title which simply states what axes you use is worthless.  For example, a title like “Growth versus Time” is an absolute no-no, because it is not complete in its description.  What is growing? Over what period of time is the measurement occurring?  On the other hand, a title like “Growth patterns of 57 Native Indiana Corn plants over 3.2 months” is acceptable.

B)      APPROPRIATE LABELS FOR THE X AND Y AXES:
These are essential to show the reader exactly what things you are talking about, as well as to show what information is being shown by which axis.  The label should be a phrase which accurately describes exactly what it is that is being described.  For example, “ Heights of group members” is preferred over “Heights” because it is much more complete in its description.

C)  APPROPRIATE SCALES ON BOTH AXES:
Scales need to be carefully chosen.  It is not only inappropriate, but downright incorrect, to have points outside the area of the ruled graph paper.  Also, distances between points cannot vary along the same axis.  (This means that a given distance always stands for a given number of units on an axis).  Under very special conditions, if the range of points is really large, you may skip an intervening space between two points, but you have to indicate what you have done by an appropriate method.

D)  APPROPRIATE UNITS:
This has some overlap with (C) above.  Using the right units gives your graph a good spread of points, and makes it easier for the reader to assimilate the knowledge.  For example, if you were weighing some really small objects, it would be inappropriate to use kilograms as the unit of measurement, for two reasons: (a) the weight would not be accurate, and (b) the graph would not show a good spread of points.

E)  AN APPROPRIATE KEY:
Use different symbols for different data.  For example, if you were going to show the height of a grass plant, a tree, and a tomato plant over time, you would use a different symbol for each plant.  The key needs to reflect this, and explain which symbol you have chosen for each plant.

Finally, let’s talk about four more things associated with line graphs: the Slope, the Line of Best Fit, Interpolation and Extrapolation.

The slope of a line is the “rise over run”.  This function is important because it allows you to calculate the rates of occurrence of phenomena.

The Line Of Best Fit (LOBF) is most easily described as a “visual average”.  Errors in measurement, be it human or experimental, result in points not always lying on one line, or an exact trend.  Points tend to be slightly scattered, and since the errors can be less than or greater than the actual value, we assume that the line that passes through all, or, failing that, the maximum number of points is the LOBF.  IF, however, the line drawn through the maximum number of points leaves a substantial number of points untouched, then the LOBF has to have the same number of points on either side.

These general rules for the LOBF are true for linear relationships.  However, in biology, you are also likely to come across LOBF’s that are not straight lines, for example in population growth curves.

Next, we’ll look at Interpolation and Extrapolation.  The part of the line that we have solid data for is drawn with a solid line.  This is the interpolated line.  Depending on whether or not the origin (0,0) is a valid data point or not, the interpolated line could start at the origin.  The part of the graph that we do not have hard data for (the part where we assume the trend continues beyond the last data point) we draw with a dotted or interrupted line.  This is the extrapolation.