To find the median of a given dataset, follow these steps:
1. Arrange the data in ascending order:
The given dataset is [tex]\([8, 11, 4, 2, 14, 9, 12, 7]\)[/tex]. First, we need to sort these numbers in ascending order:
[tex]\[
2, 4, 7, 8, 9, 11, 12, 14
\][/tex]
2. Determine the number of data points:
Count the number of elements in the sorted dataset. Here, there are 8 elements.
3. Identify if the number of data points is even or odd:
Since 8 is an even number, the median will be the average of the two middle numbers.
4. Find the middle numbers:
For an even number of data points, the middle numbers are the 4th and 5th elements in the sorted dataset:
[tex]\[
2, 4, 7, 8, 9, 11, 12, 14
\][/tex]
Here, the 4th element is 8 and the 5th element is 9.
5. Calculate the median:
Since we have an even number of elements, we take the average of the 4th and 5th elements:
[tex]\[
\text{Median} = \frac{8 + 9}{2} = \frac{17}{2} = 8.5
\][/tex]
Therefore, the median of the dataset [tex]\([8, 11, 4, 2, 14, 9, 12, 7]\)[/tex] is [tex]\(\boxed{8.5}\)[/tex].
