Answer :
To compare the mean of the population with the mean of the given sample and find the difference between them, follow these steps:
### Population Data
Here are the individual values from the population data:
[tex]\[ 4, 5, 3, 1, 3, 2, 2, 3, 5, 7, 3, 6, 3, 0, 1, 5, 0, 4, 3, 6 \][/tex]
#### Step 1: Calculate the population mean
To find the population mean, sum all the elements of the population data and divide by the number of elements.
Sum of population data:
[tex]\[ 4 + 5 + 3 + 1 + 3 + 2 + 2 + 3 + 5 + 7 + 3 + 6 + 3 + 0 + 1 + 5 + 0 + 4 + 3 + 6 = 66 \][/tex]
Number of elements in population data:
[tex]\[ 20 \][/tex]
Population mean:
[tex]\[ \frac{66}{20} = 3.3 \][/tex]
### Sample Data
Here are the individual values from the sample data:
[tex]\[ 5, 4, 6, 2, 1 \][/tex]
#### Step 2: Calculate the sample mean
To find the sample mean, sum all the elements of the sample data and divide by the number of elements.
Sum of sample data:
[tex]\[ 5 + 4 + 6 + 2 + 1 = 18 \][/tex]
Number of elements in sample data:
[tex]\[ 5 \][/tex]
Sample mean:
[tex]\[ \frac{18}{5} = 3.6 \][/tex]
### Step 3: Calculate the difference between the sample mean and the population mean
Subtract the population mean from the sample mean.
Difference:
[tex]\[ 3.6 - 3.3 = 0.3 \][/tex]
### Conclusion
The difference between the mean of the sample and the mean of the population is [tex]\(0.3\)[/tex]. Thus, the correct answer is:
[tex]\[ \boxed{0.3} \][/tex]
### Population Data
Here are the individual values from the population data:
[tex]\[ 4, 5, 3, 1, 3, 2, 2, 3, 5, 7, 3, 6, 3, 0, 1, 5, 0, 4, 3, 6 \][/tex]
#### Step 1: Calculate the population mean
To find the population mean, sum all the elements of the population data and divide by the number of elements.
Sum of population data:
[tex]\[ 4 + 5 + 3 + 1 + 3 + 2 + 2 + 3 + 5 + 7 + 3 + 6 + 3 + 0 + 1 + 5 + 0 + 4 + 3 + 6 = 66 \][/tex]
Number of elements in population data:
[tex]\[ 20 \][/tex]
Population mean:
[tex]\[ \frac{66}{20} = 3.3 \][/tex]
### Sample Data
Here are the individual values from the sample data:
[tex]\[ 5, 4, 6, 2, 1 \][/tex]
#### Step 2: Calculate the sample mean
To find the sample mean, sum all the elements of the sample data and divide by the number of elements.
Sum of sample data:
[tex]\[ 5 + 4 + 6 + 2 + 1 = 18 \][/tex]
Number of elements in sample data:
[tex]\[ 5 \][/tex]
Sample mean:
[tex]\[ \frac{18}{5} = 3.6 \][/tex]
### Step 3: Calculate the difference between the sample mean and the population mean
Subtract the population mean from the sample mean.
Difference:
[tex]\[ 3.6 - 3.3 = 0.3 \][/tex]
### Conclusion
The difference between the mean of the sample and the mean of the population is [tex]\(0.3\)[/tex]. Thus, the correct answer is:
[tex]\[ \boxed{0.3} \][/tex]
