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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.

Short Answer

Expert verified

Part (a) Ranges of the two distributions are approximately the same.

Part (b) The New Jersey distribution has a lot more exceptionally large data values than the Indiana distribution.

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Calculation

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.

03

Part (b) Step 1: Explanation

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 $0and $80,000

Then

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

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