To determine the median of the score distribution, follow these steps:
1. List the Given Scores: The given scores are:
[tex]\[
\{180, 175, 163, 186, 153, 194, 198, 183, 187, 174, 177, 196, 162, 185, 174, 195, 164, 152, 144, 138, 125, 110\}
\][/tex]
2. Sort the Scores in Ascending Order:
[tex]\[
\{110, 125, 138, 144, 152, 153, 162, 163, 164, 174, 174, 175, 177, 180, 183, 185, 186, 187, 194, 195, 196, 198\}
\][/tex]
3. Determine the Number of Scores: There are 22 scores.
4. Find the Median: Since the number of scores (22) is even, the median will be the average of the 11th and 12th scores in the sorted list.
The 11th score in the sorted list is 174, and the 12th score in the sorted list is 175.
Calculate the median:
[tex]\[
\text{Median} = \frac{174 + 175}{2} = \frac{349}{2} = 174.5
\][/tex]
5. Choose the Correct Answer: The median of the given distribution is [tex]\( \boldsymbol{174.5} \)[/tex].
Thus, the correct answer is:
D. [tex]\(174.50\)[/tex]
