1. I choose 100 WMU students at random and ask them their weight. Let the
random variable X= weight. What type of random variable is X?
Continuous
Discrete
Parameter
Variable
The correct answer is continuous.
A student asked:
I disagree. When asking students their weight no one will give a weight more
exact than to the nearest pound. I dont even think anyone knows their exact
weight to a fraction of a pound at any given time. Therefore this variable
to me is a discrete variable, because each response to the question could
only be one of so many whole numbers.
Answer: You have missed the point of a discrete random
variable.
A discrete random variable has a finite (or countable) number
of natural categories, like hair color or the number of children in
a family.
Weight is a measurement and has no natural categories.
For example,
there is nothing special about the weight 155 pounds.
In kilograms this is 70.37 kilos;
in ounces, 2480; in tons, 0.0775; on Mars where they weigh in
square-root of 2 pounds, its 219.2032 (to four places).
The Mars item makes one realize that continuous measurements
are approximations.
But keep in mind that if we had the data in each of these 5 units,
the 5 histograms would look the same.
Further, the more data I collected, the smoother the histograms
would become.
Hence, the appropriate model for weight is continuous.