To determine the median of the given data set, the step-by-step process is as follows:
Step 1: List the Data Provided
We start with the following set of numbers:
[tex]\[ 70, 50, 65, 35, 73, 74, 63, 48, 58 \][/tex]
Step 2: Arrange the Numbers in Ascending Order
We need to sort these numbers in ascending order:
[tex]\[ 35, 48, 50, 58, 63, 65, 70, 73, 74 \][/tex]
Step 3: Determine the Total Number of Data Points
Count the total number of data points in the sorted list:
The number of elements, [tex]\( n \)[/tex], is 9.
Step 4: Find the Median
Since the number of data points (9) is odd, the median will be the middle number in the sorted list. The position of the median can be found using:
[tex]\[ \text{Median position} = \left(\frac{n + 1}{2}\right) \][/tex]
For our data, this is:
[tex]\[ \text{Median position} = \left(\frac{9 + 1}{2}\right) = 5 \][/tex]
Step 5: Identify the Median
The 5th number in the sorted list is:
[tex]\[ 63 \][/tex]
Thus, the median of the given data set is [tex]\( 63 \)[/tex].
