To find the Absolute Change and the Relative Change in the Median Income for Wayne County from 2001 to 2011, follow these steps:
### Absolute Change:
1. Identify the median incomes for the years 2001 and 2011:
- Median income in 2001: \[tex]$47,231
- Median income in 2011: \$[/tex]36,559
2. Calculate the Absolute Change:
- Subtract the median income in 2011 from the median income in 2001.
[tex]\[
\text{Absolute Change} = 47,231 - 36,559
\][/tex]
[tex]\[
\text{Absolute Change} = 10,672
\][/tex]
The Absolute Change in the median income for Wayne County from 2001 to 2011 is 10,672 dollars.
### Relative Change:
3. Calculate the Relative Change:
- Use the absolute change and divide it by the median income in 2001.
[tex]\[
\text{Relative Change} = \left( \frac{\text{Absolute Change}}{\text{Median Income in 2001}} \right) \times 100
\][/tex]
[tex]\[
\text{Relative Change} = \left( \frac{10,672}{47,231} \right) \times 100
\][/tex]
4. Simplify the calculation:
- Perform the division and then multiply by 100 to convert to a percentage.
[tex]\[
\text{Relative Change} \approx 0.2259 \times 100
\][/tex]
[tex]\[
\text{Relative Change} \approx 22.6\%
\][/tex]
5. Round to the nearest tenth:
- The calculated percentage is already in the format of the nearest tenth with 22.6.
The Relative Change in the median income for Wayne County from 2001 to 2011 is approximately 22.6%.
### Summary:
- Absolute Change: 10,672
- Relative Change: 22.6%
These answers provide a clear understanding of how the median income in Wayne County has changed over the given period.
