To determine the median of a data set, follow these steps:
1. Sort the Data: Arrange all the data points in ascending order.
2. Determine the Number of Data Points (n):
- If [tex]\( n \)[/tex] is odd, the median is the middle data point.
- If [tex]\( n \)[/tex] is even, the median is the average of the two middle data points.
Let's apply these steps to the given data set.
Step 1: Sort the Data
[tex]\[ [96.6, 96.7, 96.8, 96.8, 96.8, 96.8, 97.0, 97.0, 97.1, 97.1, 97.1, 97.2, 97.2, 97.2, 97.3, 97.3, 97.3, 97.4, 97.5, 97.6, 97.6, 97.8, 97.8, 97.8, 97.9, 98.0, 98.0, 98.0, 98.1, 98.3, 98.3, 98.4, 98.4, 98.5, 98.6, 98.7, 98.9, 98.9, 99.0, 99.1, 99.2, 99.3, 99.3, 99.4, 99.4, 99.4, 99.5, 99.6] \][/tex]
Step 2: Determine the Number of Data Points
[tex]\[ n = 48 \][/tex]
Since [tex]\( n \)[/tex] is even, the median will be the average of the two middle elements.
Step 3: Find the Median
- The middle positions for an even number of elements are:
[tex]\[
\text{Middle positions: } \left(\frac{48}{2}\right) \text{ and } \left(\frac{48}{2} + 1\right) \text{ which are positions 24 and 25.}
\][/tex]
- The values at these positions in the sorted data are 97.8 and 97.9 respectively.
- Average these two values:
[tex]\[
\text{Median} = \frac{97.8 + 97.9}{2} = 97.85
\][/tex]
Thus, the median of the data set is [tex]\( 97.85 \, ^\circ \mathrm{F} \)[/tex].
