The shape of a distribution is a rough guide to whether the mean and standard de
ID: 3202230 • Letter: T
Question
The shape of a distribution is a rough guide to whether the mean and standard deviation are a helpful summary of center and spread. For which of these distributions would x and s be useful? In each case, give a reason for your decision.
(a) Percents of high school graduates in the states taking the SAT as shown below
The distribution is fairly symmetric, and therefore x and s are useful measures.
x and s are resistant measures, and therefore are not useful measures for asymmetric distributions.
x and s are useful descriptions of the center and spread for any type of distribution.
The distribution is not symmetric, and therefore x and s are not useful measures.
(b) Iowa Test scores as shown below
x and s are useful descriptions of the center and spread for any type of distribution.
x is useful but s isn't because the distribution is symmetric.
The distribution is fairly symmetric and free of outliers, and therefore x and s are useful measures.
x and s are resistant measures, and therefore they don't work for symmetric distribution.
(c) New York travel times as shown below
x and s are useful descriptions of the center and spread for any type of distribution.
s is useful but x isn't because of the tail on the left.
x and s are resistant measures, and therefore they aren't influenced by the skewed distribution.
The tail on the right strongly influences both x and s, so they are not very useful.
E o Two peaks suggest that the data include two types of states. 20 60 80 40 100 Percent of high school graduates who took the SATExplanation / Answer
answer
a
answer
option last
the data has outliers and not symmetric and therefore x and s are not the useful measures
b
option 3
the distribution is symmetric and free of outliers and therefore x and s are the useful measures
c
option
last
The tail on the right strongly influences both x and s, so they are not very useful
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