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3.2
Finding Patterns in Random Behavior
P
urpose
The role this topic plays in quantitative reasoning
While there are some things in life that can be determined precisely, most events include an element of
randomness that ultimately influences results. The most immediate implication of this is that we often
end up with a range of outcomes based upon how the random components actually end up behaving. The
stronger our skills in identifying and analyzing the nature of random behavior, the stronger our ability
to reason quantitatively.
As you saw in the likelihood activity (Section 3.1), the probability of an event changes from situation
to situation. The better we can see and predict patterns in what may appear to be a wholly random
system, the stronger our decision making can be. As an example of this, consider the stock market:
While individuals who understand little of its functioning (i.e., the triggers involved in transactions as
well as things like tendencies, and correlations) may see it as random, others with greater knowledge
believe that they can predict future behavior with some degree of confidence. Does this mean that there
is no element of randomness in the stock market? Far from it. It simply means that there are patterns in
that randomness. The key to dealing successfully with randomness is learning to identify those patterns.
Almost from the beginning of recorded history we have spent our time analyzing the phenomena around
us (e.g., crop yields, weather, markets, invasions, political elections, etc.) so that we can predict what
will happen in the future. Many of our daily decisions depend upon identifying the likely outcomes of
random behavior, for example, making business investments, choosing a type of medical care, betting
on a sporting event, or deciding on when to close a school due to weather. Each of these contexts asks
that we deal with randomness and predict future behavior. The greater our intuition and analytical skills
for understanding and modeling random behavior, the better our skills for prediction will be. This leads
to better decision making.
L
earning Goals
What you should learn while completing this activity
1. Identify the important variables impacting randomness in a situation.
2. For a given random variable, identify its pattern, what causes this pattern, and the implications
resulting from this pattern.
3. Analyze the contribution of each random variable to the overall randomness in a system.
4. Make group decisions based upon a consensus of predicted outcomes.
D
iscovery
Finding out for yourself
How random can you make a sequence of Heads (H) and Tails (T)? Check your randomness skills at the
link available on the companion website.
Use item II in the “Lay of the Land” exercise to challenge yourself to produce a random sequence of 100
Heads and Tails (H or T). Continue with the exercise to determine how random you were. Why was your
data less random than you thought? Give four reasons for your sequence’s lack of randomness. How
many different measures of randomness were used to analyze randomness?