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The median of the data set is [tex]\square \ ^{\circ}F[/tex]. (Type an integer or a decimal. Do not round.)

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\begin{tabular}{|lllllllllllll|l|}
\hline & & & & & & & & & & & \\
99.4 & 98.0 & 99.3 & 97.6 & 98.4 & 96.6 & 96.8 & 97.2 & 98.7 & 96.8 & 98.0 & 97.6 \\
98.4 & 99.3 & 98.9 & 98.5 & 97.3 & 97.2 & 96.7 & 99.4 & 99.1 & 97.3 & 99.0 & 97.3 \\
97.8 & 99.2 & 98.3 & 98.3 & 97.1 & 97.1 & 98.9 & 97.2 & 97.9 & 99.5 & 97.0 & 98.0 \\
97.0 & 98.1 & 97.8 & 97.8 & 97.1 & 99.4 & 96.8 & 97.4 & 97.5 & 99.6 & 96.8 & 98.6 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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].

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