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According to the U.S. Census, the median individual yearly income for whites in the United States was \(\$ 33,808\) in \(1990,\) almost three times the median individual yearly income for Hispanics, which was \(\$ 12,028\) for that same year. In \(2008,\) the median income for whites increased to \(\$ 35,120\) and for Hispanics to \(\$ 16,417\). a. Show how the researcher got the value to be approximately \(3,\) and explain what summary measure is estimated by this value. b. Calculate the same value as part a for the 2008 numbers. c. Why do you think the Census Bureau used the median instead of the mean for this comparison? \(^{12}\)

Short Answer

Expert verified
The ratio was 2.81 in 1990 and 2.14 in 2008. Median is used to avoid the influence of outliers.

Step by step solution

01

Understand the Problem

In this problem, we need to understand how the researcher got the approximation of the value '3' as a factor, and what measure it estimates. Then, repeat the same calculation for 2008, and comment on why the median was used over the mean.
02

Calculate Ratio for 1990 Incomes

To find the approximate ratio the researcher mentioned, divide the median income of whites by the median income of Hispanics for 1990: \[ \frac{33,808}{12,028} \approx 2.81 \] This shows that the median income for whites was about 2.81 times higher than Hispanics in 1990. This ratio provides an estimate of relative income disparity between these groups.
03

Calculate Ratio for 2008 Incomes

Apply the same process for the 2008 figures by dividing the median income of whites by the median income of Hispanics: \[ \frac{35,120}{16,417} \approx 2.14 \] Therefore, in 2008, the median income for whites was about 2.14 times higher than that for Hispanics.
04

Explanation on Use of Median

The median is used over the mean to compare incomes because it is less sensitive to extreme values and skewed data. Incomes often have outliers or high variance, so the median provides a more accurate representation of a typical (central) income.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Income Disparity
Income disparity refers to the difference in income levels between different groups in a society. It's an important concept because it highlights economic inequality. In the context of the given exercise, we're looking specifically at the difference in median incomes between whites and Hispanics in the United States during 1990 and 2008.
One way to measure income disparity is through the calculation of a ratio, which compares the median incomes of two groups. For instance, if we say that the income disparity ratio was 2.81 in 1990, this means that the median income for whites was 2.81 times higher than that for Hispanics.
This measurement helps illuminate the extent of income inequality between groups and can guide policies aimed at reducing these disparities. It's crucial to understand that income disparity impacts access to resources and opportunities for different groups, which can influence numerous aspects of life including education, healthcare, and employment.
Decoding U.S. Census Data
The U.S. Census Bureau is a key source of data about the American people, including income statistics. Conducted every ten years, the census collects comprehensive data that helps to inform policy decisions and allocate government resources.
When it comes to income data, the Census provides figures such as median income, which can be used to assess economic trends and disparities. The median income is a value that divides a population into two equal groups, half earning more than the median and half earning less. This is particularly useful because it gives a better picture of the 'typical' income, avoiding distortions by extremely high or low values.
In analyzing the data for 1990 and 2008, the exercise used median income statistics to discern income disparities between whites and Hispanics. Such data is crucial for understanding how economic circumstances may have changed over time and for pinpointing where policy interventions may be necessary.
Essentials of Ratio Calculation
Ratio calculation is a straightforward mathematical process used to compare two quantities. In the exercise, it's used to compare the incomes of white and Hispanic populations, providing a clear picture of the income disparity between the two groups.
To calculate the income ratio, divide the median income of one group by the median income of another. For 1990, dividing the median income of whites (\(33,808\)) by that of Hispanics (\(12,028\)) gives approximately 2.81. Similarly, for 2008, the calculation (\(\frac{35,120}{16,417}\)) results in a ratio of about 2.14.
This method allows for a simple yet effective comparison that highlights disparities. It's especially useful in socio-economic analyses where it’s important to understand relative differences rather than absolute numbers.

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Most popular questions from this chapter

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