Questions & Answers on the Material of Stat 160

  1. Question: This was from a prequiz:

    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.