Accuracy and Precision
What’s a Cup of Coffee?
Suppose a friend invited you out to dinner at an expensive,
five-star, French restaurant, and suppose you decided to order a cup of coffee
along with your meal. How large do you think your cup of coffee might be?
Maybe you would get a few ounces of coffee in a small cut-glass cup like this
one.
Now, suppose you are on your way to school in the morning (after an all-nighter
cramming for a test?) and decide to stop at a local gas station for a cup of
coffee. How large do you think your cup of coffee might be? Maybe your
cup of coffee would be as large as this cup, or maybe even larger!
Suppose Student Tribunal decides to have a bake sale, and you are asked to make
a coffee cake to donate. If your coffee cake recipe calls for 1 C of coffee
as one of the ingredients, which of these two cups would you use to measure
that coffee? Which one holds a cup of coffee? Both? Neither? Are there
better alternatives? Is there something else that might be better to use?
By now, you might be thinking it would be better to use a measuring cup, but
think about why. I can think of a couple reasons. While the small
cup might hold 3 or 4 oz of liquid, and the big cup might hold 12 or 24 oz,
the measuring cup is designed to hold exactly 8 oz. While each of the first
two cups was designed to hold a “cup” of liquid, the measuring cup was
specifically designed to measure 1 C (8 oz) of liquid, and it has
lines on it for just that purpose. Thus, we can say that the measuring cup
is more accurate than the other two.
The accuracy of a
measurement is how close that number is to the accepted true value. Thus,
the measuring cup is more accurate because its “1 C” of liquid is
closest to the accpted true value of 8 oz. If all you want to do is drink
a “cup” of coffee, accuracy is not as important and any of these cups will do.
However, in a situation (such as when following a recipe) where accuracy is
important, it is necessary to use the more-accurate, measuring cup. Different
levels of accuracy are important in different situations. For example, the
level of accuracy used by a pharmacist when mixing up a prescription would
need to be greater than the accuracy used by someone who is “just” baking a
cake.
Suppose that Student Tribunal needs you to bake three coffee cakes for their bake sale. That means you need to measure 1 C of coffee three times. Which piece of glassware would be easiest to fill to the same level on three different occasions? You might, again, choose the measuring cup because it has lines on it so you can fill it to the 1-C line three times. Thus, the measuring cup is the most precise. Precision is how close a group of numbers are to each other. While, in general, it might be true that the most accurate glassware is also the most precise, that might not always be the case. Consider, for example, that you could place a line on either the small cup or the big cup to facilitate filling that cup to that mark multiple times. That line might turn out to be very precise, in that the multiple measurements are close to each other, but be nowhere near 1 C, and thus not very accurate.
Lab Glassware
In a biology, there is a variety of different types of glassware, used for
different purposes. Here is a 250-mL beaker. Notice several things about
this beaker. While it is labeled as being a 250-mL beaker, notice that the
lines only go up to 200 mL. Where do you suppose the 250-mL mark is? Take
time to look closely at the lines marked on this beaker so that you understand
how many milliliters of liquid each line represents. For example, to where
would you fill this beaker if you wanted 83 mL of liquid? Notice
that about half-way up, there is a line that claims to be the 100-mL mark, so
if you fill the beaker to that point, you should, allegedly, have 100 mL of
water.
Here’s another piece of glassware called a graduated cylinder. This particular one is a 100-mL graduated cylinder. Again, take time to look at the lines and understand how many milliliters each represents. Notice the plastic base for support, and more importantly the plastic collar. Many people do not realize the importance of the collar, and thus either slide it down to an ineffective position or remove it. The purpose of the plastic collar is to try to prevent chipping or breakage in the event that the cylinder tips over (it will do nothing to prevent breakage if the cylinder is headed towards the floor), and thus, should remain near the top of the cylinder where it is able to effectively prevent the lip of the cylinder from hitting the tabletop. Notice that the top line claims to be the 100-mL mark, so if you fill the graduated cylinder to that point, you should, allegedly, have 100 mL of water.
This piece of glassware is called a volumetric flask. Notice that this one
is labeled as being a 100-mL volumetric flask, and that there is only one
line on the neck of this flask, so presumably, that is the fill-line for
100 mL of liquid.
The Scientific Method
To solve problems and make scientific discoveries, scientists use the Scientific Method.
Some Further Planning and Information
First, I guess I better figure out how much 100 mL of water is supposed to weigh. Come to think of it, any impurities, minerals, etc. in the water could change its weight, so I better plan on using distilled water (which may be abbreviated as “dH2O.” Hey, I remember something from my chemistry classes about 1 mL of water weighing 1 g. Oh, that won’t work though, because I just remembered, that’s only good at 4° C. I guess some place like a chemistry handbook would be a good place to check for that information. So, let’s see. . . the density of water does vary with temperature, so I’ll need to know what room temperature is. The book says the density of distilled water at 25° C (= 77.0° F, so that sounds close enough) is 0.99707 g/mL. That means 100 mL of water should weigh about 99.71 g at a room temperature of about 25° C.
Come to think of it, it won’t work to just pour some water into the various pieces of glassware, then weigh them, because the glass weighs something, too. Thus, I’m going to have to weigh each piece of glassware dry, first, then subtract to get the actual weight of the water. Then too, I suppose all the 250-mL beakers (graduated cylinders, volumetric flasks) in the lab contain different amounts of glass and weigh different amounts, so I better plan on keeping track of the one, specific one that I, personally, am using. Oh, yeah, for each container, I better also plan on dumping out some of the water, refilling the container, and re-weighing it several times (3 would be a good number) so I can also see which is the most precise.
I just thought of another issue I’ll need to figure out. How
will I know if I have correctly filled each piece of glassware? Yeah, I know
I have to fill each one to the 100-mL line, but wow, look how thick those
lines on that beaker are! There must be an “official” way to do fill the
glassware so I do it the same way every time.
So, here’s the rule to follow: the bottom of the meniscus has to touch the
top of the line. Glass is hydrophilic, so water in a glass container
is attracted to the glass, forming a curved surface. That curved water
surface is called a meniscus. Thus, the official way to fill
glassware, to account for both the curve of the meniscus and the thickness
of the fill-lines, is to carefully line up the bottom of the meniscus with
the top of the desired line. Similarly if someone is using a glass container
to measure the volume of an “unknown” amount of water, the reading should
be taken at the bottom of the meniscus.
I guess, if I need to weigh the glassware, I better know how to use a balance.
Recording Your Data
For each of the three pieces of glassware, you should set up a chart like this in your lab notebook. One chart like this is needed for the beaker, one for the graduated cylinder, and one for the volumetric flask. Remember that each piece of glassware is being tested 3 times.
Put the name of the type of glassware being tested here. | |||
Trial # | I | II | III |
Wt. of glassware + water |
|||
(Since it is only possible to weigh each piece of glassware dry one time prior to putting water in it, the “dry-weight” number used in all three of the following spaces will be the same.) | |||
— Wt. of glassware |
|||
Wt. of water |
Then, after obtaining all the necessary weights, it will also be necessary to calculate the mean and standard deviation for the weight of water in each of these pieces of glassware. The mean weight of water in each container may be compared with the theoretical weight of 99.71 g (assuming 25° C) to determine which of the three is closest, therefore most accurate. Since standard deviation is a measure of how spread out the numbers in a group of data are, a smaller standard deviation is an indication of greater precision, while a larger standard deviation is an indication of less precision. Construction of a table such as the following will aid you in doing these calculations.
Trial # | Wt of H2O | — x̄ | = deviation | dev to + |
I | wt = | (copy avg) | wt – x̄ = | |wt – x̄| = |
II | wt = | (copy avg) | wt – x̄ = | |wt – x̄| = |
III | wt = | (copy avg) | wt – x̄ = | |wt – x̄| = |
Σ = | tot | tot | ||
÷ 3 = x̄ | avg | avg = m dev |
Submit Your Data Online
Once you have done all your calculations, please submit your data online. This will allow collection and comparison of data from students in numerous classes. You may also view the cumulative class data.
Other Things to Include in Your Notebook
Make sure you have all of the following in your lab notebook: