Question

The shape of a distribution is a rough guide to whether the mean and standard deviation are a helpful summary of center and variability. Review each of the distributions and determine whether the measures and s would be useful. (a) The figure shows percents of high school graduates in the United States taking the SAT Two peaks suggest that the data include two types of states. 2 20 40 60 80 100 Percent of high school graduates who took the SAT

Answer 1

a.

$\small \bar x$ and s would not be useful because the graph is not symmetrical around the two peaks.

For percent of high school graduates in the states taking the SAT distribution, $\small \bar x$ and s are not useful.

As we can see from the histogram that the data is not symmetric and mean and standard deviation are useful when data is symmetric and normally distributed. So, in this case mean and standard deviation are not helpful summary of center and variation.

b.

$\small \bar x$and s are useful descriptions of the center and spread for any type of distribution.

For Iowa test score, $\small \bar x$ and s are useful.

As we can see from the histogram that the data is symmetric and normally distributed. So, in this case mean and standard deviation are helpful summary of center and variation.

c.

$\small \bar x$ and s are not useful measures because the distribution is strongly right-skewed.

For New York times travel, $\small \bar x$ and s are not useful.

The data is displayed in the form of box plot. And to show center and variability in box plot median is used.