Answer :
To fill in the missing unemployment rates (\%) in the given data set, we need to calculate the unemployment rate for each year using the provided data for the civilian labor force and the number of unemployed. The unemployment rate can be determined using the formula:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{\text{Number of Unemployed}}{\text{Civilian Labor Force}} \right) \times 100 \][/tex]
Let's calculate the unemployment rate step by step for each year where it is missing:
1. 2003:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{8774}{146510} \right) \times 100 \approx 5.99 \% \][/tex]
2. 2004:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{8149}{147401} \right) \times 100 \approx 5.53 \% \][/tex]
3. 2005:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{7591}{149320} \right) \times 100 \approx 5.08 \% \][/tex]
4. 2006:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{7001}{151428} \right) \times 100 \approx 4.62 \% \][/tex]
5. 2007:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{7078}{153124} \right) \times 100 \approx 4.62 \% \][/tex]
6. 2008:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{8924}{154287} \right) \times 100 \approx 5.78 \% \][/tex]
7. 2009:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{14265}{154142} \right) \times 100 \approx 9.25 \% \][/tex]
8. 2010:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{14825}{153889} \right) \times 100 \approx 9.63 \% \][/tex]
9. 2011:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{13747}{153617} \right) \times 100 \approx 8.95 \% \][/tex]
10. 2012:
The number of unemployed is not provided for this year, so the unemployment rate cannot be calculated.
Summarizing, the filled data set with calculated unemployment rates is:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline Year & Civilian Labor Force & \# Unemployed & Unemployed Rate (\%) \\ \hline 2002 & 144863 & 8,378 & 5.78 \\ \hline 2003 & 146510 & 8,774 & 5.99 \\ \hline 2004 & 147401 & 8,149 & 5.53 \\ \hline 2005 & 149320 & 7,591 & 5.08 \\ \hline 2006 & 151428 & 7,001 & 4.62 \\ \hline 2007 & 153124 & 7,078 & 4.62 \\ \hline 2008 & 154287 & 8,924 & 5.78 \\ \hline 2009 & 154142 & 14,265 & 9.25 \\ \hline 2010 & 153889 & 14,825 & 9.63 \\ \hline 2011 & 153617 & 13,747 & 8.95 \\ \hline 2012 & 154974 & N/A & N/A \\ \hline \end{tabular} \][/tex]
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{\text{Number of Unemployed}}{\text{Civilian Labor Force}} \right) \times 100 \][/tex]
Let's calculate the unemployment rate step by step for each year where it is missing:
1. 2003:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{8774}{146510} \right) \times 100 \approx 5.99 \% \][/tex]
2. 2004:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{8149}{147401} \right) \times 100 \approx 5.53 \% \][/tex]
3. 2005:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{7591}{149320} \right) \times 100 \approx 5.08 \% \][/tex]
4. 2006:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{7001}{151428} \right) \times 100 \approx 4.62 \% \][/tex]
5. 2007:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{7078}{153124} \right) \times 100 \approx 4.62 \% \][/tex]
6. 2008:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{8924}{154287} \right) \times 100 \approx 5.78 \% \][/tex]
7. 2009:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{14265}{154142} \right) \times 100 \approx 9.25 \% \][/tex]
8. 2010:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{14825}{153889} \right) \times 100 \approx 9.63 \% \][/tex]
9. 2011:
[tex]\[ \text{Unemployment Rate (\%)} = \left( \frac{13747}{153617} \right) \times 100 \approx 8.95 \% \][/tex]
10. 2012:
The number of unemployed is not provided for this year, so the unemployment rate cannot be calculated.
Summarizing, the filled data set with calculated unemployment rates is:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline Year & Civilian Labor Force & \# Unemployed & Unemployed Rate (\%) \\ \hline 2002 & 144863 & 8,378 & 5.78 \\ \hline 2003 & 146510 & 8,774 & 5.99 \\ \hline 2004 & 147401 & 8,149 & 5.53 \\ \hline 2005 & 149320 & 7,591 & 5.08 \\ \hline 2006 & 151428 & 7,001 & 4.62 \\ \hline 2007 & 153124 & 7,078 & 4.62 \\ \hline 2008 & 154287 & 8,924 & 5.78 \\ \hline 2009 & 154142 & 14,265 & 9.25 \\ \hline 2010 & 153889 & 14,825 & 9.63 \\ \hline 2011 & 153617 & 13,747 & 8.95 \\ \hline 2012 & 154974 & N/A & N/A \\ \hline \end{tabular} \][/tex]
