Sure! Let's examine the set [tex]\( \text{Buc} = \{-4, -2, -1, 0, 2, 3, 4, 7\} \)[/tex].
Here are the steps to understand and work with this set:
1. Identify the set elements: The set [tex]\( \text{Buc} \)[/tex] contains the elements [tex]\(-4, -2, -1, 0, 2, 3, 4,\)[/tex] and [tex]\(7\)[/tex].
2. Order of elements: This list of numbers seems to be arranged in ascending order:
[tex]\[
-4 < -2 < -1 < 0 < 2 < 3 < 4 < 7
\][/tex]
3. Properties:
- Negative numbers: [tex]\(-4, -2, -1\)[/tex]
- Zero: [tex]\(0\)[/tex]
- Positive numbers: [tex]\(2, 3, 4, 7\)[/tex]
4. Count the elements: There are a total of 8 elements in this set.
5. Mean of the set:
To find the mean, you sum up all the elements and then divide by the number of elements:
[tex]\[
\text{Sum} = -4 + (-2) + (-1) + 0 + 2 + 3 + 4 + 7 = 9
\][/tex]
[tex]\[
\text{Mean} = \frac{\text{Sum}}{\text{Number of elements}} = \frac{9}{8} = 1.125
\][/tex]
6. Range of the set:
The range is the difference between the largest and smallest elements in the set:
[tex]\[
\text{Range} = 7 - (-4) = 7 + 4 = 11
\][/tex]
7. Median of the set:
Since there are 8 elements (which is an even number), the median will be the average of the 4th and 5th elements:
[tex]\[
\text{4th element} = 0, \quad \text{5th element} = 2
\][/tex]
[tex]\[
\text{Median} = \frac{0 + 2}{2} = 1
\][/tex]
8. Mode of the set:
Since all elements appear only once, there is no mode.
9. Standard Deviation (if needed):
To calculate the standard deviation, you would use the formula:
[tex]\[
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}
\][/tex]
But let's not get into detailed computations here unless required.
These steps provide a detailed analysis and handling of the set [tex]\( \text{Buc} \)[/tex]. This should cover any basic operations or insights you need for this particular set. If you have more specific questions or need further calculations, feel free to ask!
