Chapter 2.2, Problem 92E

(a)

To determine

Comparison of two distributions ranges.

Answer to Problem 92E

Ranges of the two distributions are approximately the same.

Explanation of Solution

Given information:

  

In the Indiana distribution, the data values range from $0 to approximately $160,000. It has been shown in the dotplot that the leftmost dot corresponds to $0 and the rightmost dot corresponds to approx. $160,000.

In the New Jersey distribution, the data values range from approximately $5000 to approximately $165,000. It has been shown in the dotplot that the leftmost dot corresponds to approx. $5,000 and the rightmost dot corresponds to approx. $165,000.

Now,

The difference between largest data value and smallest data value gives the range.

For Indiana:

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

For New Jersey:

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

Note that

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

Thus,

The two distributions have approx. equal ranges.

(b)

To determine

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

Answer to Problem 92E

When compared to the Indiana distribution, the New Jersey distribution contains a lot more unusually large data values.

Explanation of Solution

Given information:

  

Note that

The Indiana distribution consists of only one outliner (approx. at $160,000), since there is only one point which is separated by a large gap from the other dots.

Although, the New Jersey distribution seems to have more outliners, since between $0 and $80,000, a lot more dots appear to be in the tail to the right of the bulk of dots.

Then

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