To address the problem, we need to find two statistical measures from the given data set: the mean and the median.
The data set given is: [tex]\( 8, 9, 2, 2, 3, 5 \)[/tex].
### Finding the Mean:
The mean (often termed as the average) is calculated by summing all the numerical values in the data set and then dividing this sum by the total number of values in the set.
1. Sum of the data set values:
[tex]\[
8 + 9 + 2 + 2 + 3 + 5 = 29
\][/tex]
2. Number of values in the data set:
[tex]\[
6
\][/tex]
3. Calculate the mean:
[tex]\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{29}{6} \approx 4.833333333333333
\][/tex]
### Finding the Median:
The median is the middle value in a data set when it is ordered in ascending order. If the number of values is odd, the median is the middle number. If the number of values is even, the median is the average of the two middle numbers.
1. Order the data set in ascending order:
[tex]\[
2, 2, 3, 5, 8, 9
\][/tex]
2. Identify the middle values:
Since there are 6 numbers (an even number), the median will be the average of the 3rd and 4th numbers in the ordered list.
[tex]\[
3^{\text{rd}} \text{ number} = 3 \quad \text{and} \quad 4^{\text{th}} \text{ number} = 5
\][/tex]
3. Calculate the median:
[tex]\[
\text{Median} = \frac{3 + 5}{2} = \frac{8}{2} = 4
\][/tex]
### Summary:
- The mean of the data set [tex]\( 8, 9, 2, 2, 3, 5 \)[/tex] is [tex]\(\boxed{4.833333333333333}\)[/tex].
- The median of the data set [tex]\( 8, 9, 2, 2, 3, 5 \)[/tex] is [tex]\(\boxed{4}\)[/tex].
