To solve this problem, we'll need to calculate both the mean (average) and the median number of schools for the given counties.
### Step-by-Step Solution:
1. List of Schools in Each County:
County B: 8,
County C: 4,
County D: 2,
County E: 5,
County F: 4,
County G: 4
2. Calculate the Mean Number of Schools:
The mean (or average) is calculated by summing up all the values and then dividing by the number of values.
[tex]\[
\text{Mean} = \frac{\sum \text{Number of Schools}}{\text{Total Number of Counties}}
\][/tex]
Sum of the number of schools:
[tex]\[
8 + 4 + 2 + 5 + 4 + 4 = 27
\][/tex]
Number of counties:
[tex]\[
6
\][/tex]
Mean number of schools:
[tex]\[
\frac{27}{6} = 4.5
\][/tex]
So, the mean number of schools in each county is 4.5.
3. Calculate the Median Number of Schools:
The median is the middle value in a data set when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.
First, order the number of schools in ascending order:
[tex]\[
2, 4, 4, 4, 5, 8
\][/tex]
Since there are 6 values (an even number), the median will be the average of the 3rd and 4th values.
The 3rd value is 4 and the 4th value is also 4. Therefore:
[tex]\[
\text{Median} = \frac{4 + 4}{2} = 4.0
\][/tex]
So, the median number of schools for these counties is 4.0.
### Final Filled Table and Answers
\begin{tabular}{|l|c|}
\cline { 2 - 2 } \multicolumn{1}{c|}{ Number of Schools in Each County } \\
\hline County A & Number of Schools \\
\hline County B & 8 \\
\hline County C & 4 \\
\hline County D & 2 \\
\hline County E & 5 \\
\hline County F & 4 \\
\hline County G & 4 \\
\hline
\end{tabular}
The mean is the addition of all the schools in each county divided by the number of counties. The mean number of schools in each county is [tex]\( 4.5 \)[/tex].
The median is the middle value of the data set. The median number of schools for these counties is [tex]\( 4.0 \)[/tex].
