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Q
uantitative
R
easoning &
P
roblem
S
olving
300
© 2014 Pacific Crest
O
ops
! A
voiding
C
ommon
E
rrors
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Generalizing results from convenient or non-representative sample
Example
: Eight friends buy lottery tickets and on their $2 ticket, 3 individuals didn’t win
anything, 2 people won $2, the other 3 people won $5, $50, and $1,000. I can expect
to average about $132 for every ticket I buy.
Why?
If your sample is fairly large and it comes from a random sample of the population,
it is reasonable to assume that the overall central tendency will match the central
tendency of your sample. If you use a convenient sample or a non-representative
sample, do not generalize to a larger group.
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Constructing means and medians for nominal data
Example
: A survey asks, “What is your favorite ice cream?” We pick 1: Vanilla, 2: Chocolate, 3:
Strawberry, 4: Pistachio, 5: Rocky Road, and 6: Other. We find the average is skewed
because of the popularity of vanilla and chocolate. The mean is 2.2.
Why?
If you are given categorical data, do not attempt to compute the mean or median. The
only measure that is reasonable is the mode.
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Emphasizing the mean for highly-skewed data
Example
: The average GPA of students at Phillips Exeter Academy is 8.5. But half of the
students have a GPA of at least 9.5 because the maximum GPA is 11.
Why?
Real-world data is often skewed. This is especially true with financial data such as
salaries or selling prices. The mean of skewed data is of limited value if you want to
know a typical value.
A
re You Ready?
Before continuing, you should be able to ...
I can...
OR
Here’s my question...
compute the mean for a set of data
compute the median for sets of odd and
even numbers of elements
determine the mode of a data set
determine which measure of central
tendency is best for a given data set
predict the relationship among the mean,
median, and mode of a skewed data set.