Answer :
To determine the population and sample mean for the ninth-grade dropouts per year, follow these steps:
1. Identify the Population Data:
The table provides the number of dropouts over a span of 20 years. Extract these numbers:
[tex]\[ 6, 6, 4, 4, 1, 2, 7, 6, 1, 1, 1, 3, 3, 5, 4, 5, 7 \][/tex]
2. Calculate the Population Mean:
The population mean is the average number of dropouts per year over the entire 20-year period. It can be calculated using the formula for the mean, which is the sum of all the data points divided by the number of data points.
Given that you have 20 years of data:
[tex]\[ \text{Population Mean} = \frac{\text{Sum of data points}}{\text{Number of data points}} = \frac{82}{21} = 3.882 \][/tex]
3. Identify the Sample Data:
The sample includes only the last 3 years' dropouts:
[tex]\[ 5, 7 \][/tex]
4. Calculate the Sample Mean:
The sample mean is the average number of dropouts per year for the sample data. It can be calculated similarly using the mean formula.
[tex]\[ \text{Sample Mean} = \frac{\text{Sum of sample data points}}{\text{Number of sample data points}} = \frac{16}{3} = 5.333 \][/tex]
Using these calculations, we can see:
- The population mean is approximately \(3.88\).
- The sample mean is approximately \(5.33\).
Therefore, the correct answer is:
E. The population mean is 3.88. The sample mean is 5.33.
1. Identify the Population Data:
The table provides the number of dropouts over a span of 20 years. Extract these numbers:
[tex]\[ 6, 6, 4, 4, 1, 2, 7, 6, 1, 1, 1, 3, 3, 5, 4, 5, 7 \][/tex]
2. Calculate the Population Mean:
The population mean is the average number of dropouts per year over the entire 20-year period. It can be calculated using the formula for the mean, which is the sum of all the data points divided by the number of data points.
Given that you have 20 years of data:
[tex]\[ \text{Population Mean} = \frac{\text{Sum of data points}}{\text{Number of data points}} = \frac{82}{21} = 3.882 \][/tex]
3. Identify the Sample Data:
The sample includes only the last 3 years' dropouts:
[tex]\[ 5, 7 \][/tex]
4. Calculate the Sample Mean:
The sample mean is the average number of dropouts per year for the sample data. It can be calculated similarly using the mean formula.
[tex]\[ \text{Sample Mean} = \frac{\text{Sum of sample data points}}{\text{Number of sample data points}} = \frac{16}{3} = 5.333 \][/tex]
Using these calculations, we can see:
- The population mean is approximately \(3.88\).
- The sample mean is approximately \(5.33\).
Therefore, the correct answer is:
E. The population mean is 3.88. The sample mean is 5.33.
