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Q: statistics ( Answered 5 out of 5 stars,   0 Comments )
Question  
Subject: statistics
Category: Miscellaneous
Asked by: boobee-ga
List Price: $5.00
Posted: 20 Sep 2002 14:30 PDT
Expires: 20 Oct 2002 14:30 PDT
Question ID: 67379
Ten people are asked the following two questions:  To assess the
probability that it would snow this coming winter in Scotsdale.  The
answers varied from 50% to 100%; the second question asked the ten to
assess the probability of getting a heart when a card is randomly
chosen from a fair deck of cards. All but one answered the same (25%)-
one answered (50%). Compare the variability n responses for the two
questions and explain why one is more variable than the other.
Answer  
Subject: Re: statistics
Answered By: answerguru-ga on 20 Sep 2002 15:16 PDT
Rated:5 out of 5 stars
 
Hi again boobee,

Before we look at the questions themselves, it is important to
understand the definition of variability. In essence, variability is
the extent to which a set of data collected from a random sample is
spread out. In statistics, this is often measured using the variance
and standard deviation.

Let's start with the first question:

"What is the probability that it will snow this coming winter?"

Does anyone really know that answer to this question? The answer is a
clear NO! Technology has not come far enough for us to predict the
weather accurately for more than a 5 day period. So when this question
was asked to the ten people, they had to rely on experience,
intuition, and knowledge of the region in order to provide an educated
answer. Though it is always likely that some people may have just
guessed without any reason at all! So we can expect that the
variability in the data collected will be fairly high, since it is
reasonable to expect that the experience, intuition, and knowledge of
each individual asked is different.


Now for the second question:

"What is the probability of getting a heart when a card is randomly
chosen from a fair deck of cards?"

We approach this question is a similar manner as the first one. Is
there a clear answer to this question? The answer is YES. This
probability is easily obtained using the following pieces of
information:

# of cards in a fair deck: 52
# of cards of each suit: 13

Proportion of hearts in a fair deck: 13/52 = 0.25 = 25%

Of course, everyone might not know the information needed to do this
calculation, and so there will be people who will have to rely on
other intuition, knowledge, and experiences to answer the question to
the best of their abilities. Since this information is quite widely
known and available, a large majority of people will apply it to
answer the question. Thus the variability is significantly lower than
the first question.

So to summarize, the variability of these two questions are affected
by the following factors:
1. Whether or not there is there a generally accepted "correct" answer
question
2. The extent to which the correct answer (if it exists) and/or the
information needed to acquire it are general knowledge.


Hope that clears it up...if you have any problems understanding the
information above please feel free to post a clarification.

Cheers!
answerguru-ga
boobee-ga rated this answer:5 out of 5 stars
Thanks again....It is great to have a way to check and make sure one
is on the right path to an answer -- you make that easy....

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