To find the median of the dataset [tex]\(4, 13, 10, 15, 11, 3, 5\)[/tex], follow these steps:
1. List the numbers in ascending order:
We start by sorting the numbers in the dataset from smallest to largest.
The sorted dataset is: [tex]\[3, 4, 5, 10, 11, 13, 15\][/tex]
2. Count the number of data points:
We need to determine how many numbers are in the dataset. There are 7 numbers in total.
3. Find the median:
The median is the middle value in a sorted array of numbers. Since we have an odd number of data points (7 in this case), the median is the number that is in the middle of the sorted dataset.
The middle position is given by: [tex]\(\left(\frac{7 + 1}{2}\right)\)[/tex]
Calculating this gives:
[tex]\[
\left(\frac{7 + 1}{2}\right) = \frac{8}{2} = 4
\][/tex]
So, the median is the 4th number in the sorted dataset.
4. Identify the median:
Looking at the 4th position in our sorted list [tex]\[3, 4, 5, 10, 11, 13, 15\][/tex], the number at this position is 10.
Therefore, the median of the dataset [tex]\(4, 13, 10, 15, 11, 3, 5\)[/tex] is [tex]\( \boxed{10} \)[/tex].
