To solve the question, we need to calculate the population mean and the sample mean of ninth-grade dropouts per year using the given data.
### Step 1: Calculate the Population Mean
The population mean is calculated by summing up all the values in the dataset and dividing by the number of values.
Given data of dropouts over 20 years:
[tex]\[ 7, 8, 6, 6, 6, 4, 4, 1, 2, 7, 6, 1, 1, 1, 3, 3, 5, 4, 5, 7 \][/tex]
Sum of all the dropouts:
[tex]\[ 7 + 8 + 6 + 6 + 6 + 4 + 4 + 1 + 2 + 7 + 6 + 1 + 1 + 1 + 3 + 3 + 5 + 4 + 5 + 7 = 87 \][/tex]
Number of years (N):
[tex]\[ 20 \][/tex]
Population mean:
[tex]\[ \frac{87}{20} = 4.35 \][/tex]
### Step 2: Calculate the Sample Mean
The sample includes only the last 3 years of data:
[tex]\[ 5, 5, 7 \][/tex]
Sum of the sample dropouts:
[tex]\[ 5 + 5 + 7 = 17 \][/tex]
Number of years in the sample (n):
[tex]\[ 3 \][/tex]
Sample mean:
[tex]\[ \frac{17}{3} \approx 5.33 \][/tex]
### Comparisons with Given Options
- Option A: The population mean is 4.35 and the sample mean is 5.30
- Option B: The population mean is 4.21 and the sample mean is 5.39
- Option C: The population mean is 5.30 and the sample mean is 3.75
- Option D: The population mean is 5.33 and the sample mean is 4.21
Given our calculated values:
- Population mean = 4.35
- Sample mean = 5.33
None of the given options exactly match our calculated values.
Therefore, the correct answer is:
```
None of the above
```
