Question

joaquin and trisha are playing a game in which the lower median wins the game. their scores are shown below. trishas scores: 92, 90, 55, 76, 91, 74. joaquins scores: 75, 72, 85, 62, 58, 91. which supports the conclusion that joaquin won the game? o joaquin won because the median of his scores is 73.5 and the median of trishas scores is 83. o joaquin won because the median of his scores is 83 and the median of trishas scores is 73.5. o trisha won because the median of her scores is 73.5 and the median of joaquins scores is 83. o trisha won because the median of her scores is 83 and the median of joaquins scores is 73.5.

Explanation:

Step1: Arrange Trisha's scores in ascending order

$55,74,76,90,91,92$
Since there are 6 scores (an even - numbered data set), the median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th numbers. Median of Trisha's scores $=\frac{76 + 90}{2}=83$.

Step2: Arrange Joaquin's scores in ascending order

$58,62,72,75,85,91$
Since there are 6 scores (an even - numbered data set), the median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th numbers. Median of Joaquin's scores $=\frac{72+75}{2}=73.5$.

Step3: Compare the medians

Since the lower median wins the game and $73.5<83$, Joaquin won because the median of his scores is 73.5 and the median of Trisha's scores is 83.

Answer:

Joaquin won because the median of his scores is 73.5 and the median of Trisha's scores is 83.