More money $(1.3)$ Refer to Exercise $91$

a. How do the ranges of the two distributions compare? Justify your answer.

b. Explain why the standard deviation of the total family incomes in the New Jersey sample is so much larger than for the Indiana sample.

The data values in the Indiana distribution range from $\$0$ to around $\$160,000$ The left-most dot corresponds to $\$0$, whereas the right-most dot corresponds to around $\$160,000$ as illustrated in the dot plot.

The data values in the New Jersey distribution vary from about $\$5000$ to about $\$165,000$ dollars. The left-most dot corresponds to approximately $\$5,000,$ while the right-most dot corresponds to approximately $\$165,000,$ as illustrated in the dot plot.

Now,

The range is defined as the difference between the largest and smallest data values.

For Indiana:

$Range=max.-min.=\$160,000-\$0=\$160,000$

For New Jersey:

$Range=max.-min.=\$165,000-\$5,000=\$160,000$

Note that

For both the distributions, the range is approx. $\$160,000$

Thus,

The two distributions have approx. equal ranges.

Because there is just one point that is separated by a considerable gap from the other dots, the Indiana distribution has only one outliner (about $\$160,000$).

Although the New Jersey distribution appears to have more outliners because there are a lot more dots in the tail to the right of the majority of dots between $\$0$and $\$80,000$

Then

The standard deviation $\left(\sigma \right)$for the New Jersey sample will be higher because the distribution has a lot more unusually large values, and the standard deviation$\left(\sigma \right)$ is influenced by unusually large (or small) values.