BIOL 1406

PreLab 1.1

What are random variables?

Scientific investigation is based on observations.  Observations refer to any information we collect about the physical universe using our senses (sight, sound, smell, taste, and touch.)  The factors or conditions being observed are called random variables (or experimental variables) because they can vary from one experiment to the next.  A random variable can be either discrete or continuous.  For example: 

  1. A pair of dice is tossed ten times. The random variable X is defined as the number of times we get a 7.  Because X can only take certain values (0, 1, 2, 3, 4, ….10) it is a discrete random variable.
     
  2. The length of a sheet of paper is measured. The random variable Y is defined as its length in centimeters. Because Y can take any positive real value, it is a continuous random variable.

 

Dice

 

Your Turn

Think about each of the random variables listed below. For each example, enter "d" in the answer box if the variable is discrete or enter "c" if it is continuous. Make sure you can explain your answers.

You can move your cursor over the hotspots to get a  "Hint" or "Check your answer."
The number of birds in a nest. Hint Check your answer.
The time it takes to drive from Austin to Dallas. Hint Check your answer.
Your body temperature. Hint Check your answer.
The amount of urine you produce each day. Hint Check your answer.
The number of bones in your hand. Hint Check your answer.

 

Your Turn

Try to think of some additional examples of discrete and continuous random variables. Enter at least 2 examples in each space provided.

You can move your cursor over the hotspots to get a "Hint" or "Check your answer."
Give an example of a discrete random variable. Hint Check your answer.
Give an example of a continuous random variable. Hint Check your answer.

A major advance in science occurred when scientists realized the advantage of describing observations of random variables quantitatively (using specific numbers) rather than qualitatively (descriptions without the use of specific numbers).  For one thing, quantitative observations tend to be more objective than qualitative observations.  In addition, quantitative observations can be analyzed using various mathematical and statistical techniques that can give us important information about the random variables we are studying and the exact relationships between those variables.

Your Turn

Answer the three questions below. Then compare your answers with the examples provided.

You can move your cursor over each hotspot to "Check your answer.".
Give a quantitative description of your weight. Check your answer.
Give a qualitative description of your weight. Check your answer.
Is weight a continuous random variable or a discrete random variable?  Check your answer.

Measuring is simply a way of quantifying our observations of a random variable (i.e. assigning a specific numerical value to each observation).  Usually, when we make measurements, each observation is described in terms of BOTH a number AND a unit of measurement.  The information that is recorded to describe our observations (either quantitatively or qualitatively) is referred to as data.  This lab focuses on a number of important principles and techniques involved in measuring random variables and in analyzing quantitative data.

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