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Household incomes The cumulative relative frequency graph describes the distribution of median household incomes in the 50 states in a recent year.

a. The median household income in North Dakota that year was $55,766Is North Dakota an unusually wealthy state?

b. Estimate and interpret the 90th percentile of the distribution.

Short Answer

Expert verified

Part (a) North Dakota is not an unusually wealthy state.

Part (b) The median household income of 90% of all the states is less than $64,000

Step by step solution

01

Part (a) Step 1: Given information

The figure is

02

Part (a) Step 2: Concept

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

03

Part (a) Step 3: Explanation

First

Because $55,766 is about fifty-six thousand dollars, draw a vertical line intersecting the horizontal axis at 56

Then

Draw a horizontal line through the curve and the vertical line's intersection.

Note that

At 68.4, the horizontal line intersects the vertical axis roughly.

That implies

Around 68.4% of the states have lower median household incomes.

And

The rest 31.6% of the states have higher median household income.

Since

A percentage less than 5% is considered to be small.

As a result, North Dakota is not typically wealthy, as its population of 31.6 percent cannot be regarded as insignificant.

04

Part (b) Step 1: Explanation

The data value represented by the Xth percentile has x% of the data values below it.

That implies

The 90th percentile represents a data value with 90% of the data values below it.

Now,

Draw a horizontal line at 90 degrees to the vertical axis.

Then

Draw a vertical line through the curve and the horizontal line's intersection.

Note that

At 64, the vertical line touches the horizontal axis roughly.

That implies

The 90th percentile is roughly at $64,000

Thus,

The median household income of 90% of all the states is less than $64,000

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