I asked a full professor of mathematics at LSU to do assignment 1 to see what would happen.

The assignment was to:

• find an article in the popular press that features a QUANTITATIVE VARIABLE,
• identify the variable,
• describe the class of situations in which it can be measured and the the ways it's measured and
• comment on its meaning and significance.

He claims he worked in a hurry. Here is what he wrote:

Seat Belt Usage: Study of a Quantitative Variable

The number giving the percentage of drivers wearing seat belts in a given geographical region and a given year is a good example of a quantative variable. If we fix the geographical region, then the variable depends on the year in which the data is collected; if we fix the year, then the variable depends on the geographical region which is chosen.

It is not entirely clear how this quantitative variable is measured. First, one has to decide whether one is measuring only the driver or whether one is measuring only passengers, or both driver and passengers. Next, the law in most states only requires front-seat occupants to buckle up, so it must be decided whether one counts people in front seat only, or people in all seats.

To fix ideas, let us say that we consider all the occupants in all seats in the vehicle. Even then, it is unclear how the data is collected. One possibility is to look at data from accident reports, since these reports routinely ask whether seat belts were worn. For the purposes of collecting our data, if a car with, say, four occupants, is involved in an accident, we would count that as four different accidents. Then, for a given region and year, we would form the quotient

number of accidents in which occupant wore seat belt
-------------------------------------------------------------
number of accidents in given region and year

and express the result as a percentage. We would then simply assume that this percentage is the correct percent for all drivers. Computing in this way ignores the possibility that-- perhaps-- drivers not having accidents always wear seat belts!

Another possibility for measuring our quantitative variable is to look at police summonses. Again, if a vehicle contains four occupants, we count that as four distinct cases. Then we divide the number of summonses issued for any driving offense in which the occupant is wearing a seat belt by the total number of summonses issued (once again, a summons for a car with two occupants is counted as two summonses). Again, one assume that this fraction, expressed as a percent, actually measures our quantitative variable.

Finally, one could have observers take a random sample on various days and various locations throughout the region; say have trained observers collect data at city intersections (and also on country roads and in various residential locations) and simply divide the number of seat-belt wearers by the total number of occupants passing by. The resulting quotient, expressed as a percent, would give us a measure of our quantitative variable. If done this way, it would be necessary to have a reasonable estimate of how accurately the observer can count; it may be especially difficult to determine whether back-seat occupants in fast-moving vehicles are wearing seat belts.