Let's carefully solve the given problems step-by-step. Here's the matrix we are working with:
[tex]\[
\begin{array}{|l|l|l|l|}
\hline
6 & 7 & 8 & 9 \\
3 & 8 & 7 & 5 \\
\hline
\end{array}
\][/tex]
First, we will list all the elements in the matrix in a single array:
[tex]\[ [6, 7, 8, 9, 3, 8, 7, 5] \][/tex]
### (i) Finding the Range
1. Identify the smallest and largest values in the array.
- Minimum value: 3
- Maximum value: 9
2. Calculate the range by subtracting the minimum value from the maximum value:
[tex]\[ \text{Range} = 9 - 3 = 6 \][/tex]
Therefore, the range is [tex]\( \boxed{6} \)[/tex].
### (ii) Finding the Median
1. Sort the elements in the array:
[tex]\[ [3, 5, 6, 7, 7, 8, 8, 9] \][/tex]
2. Determine the median value.
- Since there are 8 elements, which is an even number, the median is the average of the 4th and 5th elements in the sorted list.
- 4th element: 7
- 5th element: 7
- Median calculation:
[tex]\[ \text{Median} = \frac{7 + 7}{2} = \frac{14}{2} = 7.0 \][/tex]
Therefore, the median is [tex]\( \boxed{7.0} \)[/tex].
### (iii) Finding the Mean
1. Sum all the elements in the array:
[tex]\[ 6 + 7 + 8 + 9 + 3 + 8 + 7 + 5 = 53 \][/tex]
2. Divide the total sum by the number of elements:
[tex]\[ \text{Mean} = \frac{53}{8} = 6.625 \][/tex]
Therefore, the mean is [tex]\( \boxed{6.625} \)[/tex].
### Summary:
- Range: [tex]\( 6 \)[/tex]
- Median: [tex]\( 7.0 \)[/tex]
- Mean: [tex]\( 6.625 \)[/tex]
These are the calculated results for the given matrix.
