Absolutely. Let's go through the calculations step by step.
1. Mean of the Sample:
The sample data provided is:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline 4 & 1 & 5 & 3 \\
\hline
\end{array}
\][/tex]
To calculate the mean of the sample data:
[tex]\[
\text{Sample Mean} = \frac{ \sum \text{Sample Values} }{ \text{Number of Sample Values} }
\][/tex]
Adding the values:
[tex]\[
4 + 1 + 5 + 3 = 13
\][/tex]
Dividing by the number of values (which is 4):
[tex]\[
\text{Sample Mean} = \frac{13}{4} = 3.25
\][/tex]
2. Mean of the Population:
The population data provided is:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline 2 & 5 & 10 & 2 \\
\hline 4 & \text{None} & 5 & \text{None} \\
\hline 8 & 1 & 4 & 3 \\
\hline
\end{array}
\][/tex]
First, we ignore the `None` values and gather all the numerical values:
[tex]\[
\{2, 5, 10, 2, 4, 5, 8, 1, 4, 3\}
\][/tex]
Adding the population values:
[tex]\[
2 + 5 + 10 + 2 + 4 + 5 + 8 + 1 + 4 + 3 = 44
\][/tex]
Counting the number of values (which is 10):
[tex]\[
\text{Population Mean} = \frac{44}{10} = 4.4
\][/tex]
3. Difference between the Mean of the Sample and the Population:
The difference is calculated as follows:
[tex]\[
\text{Mean Difference} = \text{Sample Mean} - \text{Population Mean}
\][/tex]
Substituting the values we found:
[tex]\[
\text{Mean Difference} = 3.25 - 4.4 = -1.15
\][/tex]
Thus, the mean of the sample is [tex]\(3.25\)[/tex], the mean of the population is [tex]\(4.4\)[/tex], and the difference between the sample mean and the population mean is [tex]\(-1.15\)[/tex].
