Hands-on Activity:
Compare the Aspirins

Relevant National Science Education Standards and
New Jersey State Science Curriculum Standards

This activity is best suited for honors-level students, because of the advanced mathematics involved. The students will weigh 20 aspirin tablets of both a name brand and a generic aspirin. For each set of weights they will calculate a standard deviation, and from the standard deviation conclude which aspirin, name brand or generic, was made with better quality control.

The smaller the standard deviation, the closer each tablet comes to the average value. You might have the students plot the standard deviation on a Gaussian curve where the center of the curve is defined as (x - m)/s = 0. 68.26% of all the values (in a theoretically infinite population) fall within the limits 0 ±s, 95.0% includes all values 0 ±2s, and 99.74% includes all values 0 ±3s.

When a worker goes into the laboratory and measures a quantity, or when a tablet of a given mass is "spit" off the assembly line, we presume that the result is one of an infinite population of such values that one might obtain in doing this exercise for an eternity. The chances are roughly 2 to 1 that the measured values will be no further than s from the mean (average) of the infinite population, and about 20 to 1 that the result will lie in the range 0 ±2s. In practice, we can never find s for an infinite population, but the standard deviation of a finite number of observations may be taken as an estimate of s. We may thus predict something about the likelihood of the occurrence of an error of a certain magnitude in the work of a particular individual or tablet batch once enough measurements have been performed to permit estimation of the characteristics of a particular infinite population.

In nonstatistical terms, suppose a set of 10 aspirin tablets is measured thus:

	Tablet mass x (g)	d = x - m	d2
	0.4325	-0.0021	0.00000441
	0.4322	-0.0024	0.00000576
	0.4457	+0.0111	0.00012321
	0.4298	-0.0048	0.00002304
	0.4355	+0.0009	0.00000081
	0.4367	+0.0021	0.00000441
	0.4402	+0.0056	0.00003136
	0.4288	-0.0058	0.00003364
	0.4279	-0.0067	0.00004489
	0.4368	+0.0022	0.00000484
Average mass m	0.4346	S d2	0.00027637

The standard deviation is shown on a Gaussian curve on the right.

Relevant National Science Education Standards

Science and Technology — The activity shows the application of abstract statistics to the practical problem of quality control in aspirin production.