Question

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

Explanation:

Step1: Arrange Joaquin's scores in ascending order

$58,62,72,75,85,91$

Step2: Calculate Joaquin's median

Since there are 6 scores (an even - numbered set), the median is the average of the 3rd and 4th ordered values. So, $\frac{72 + 75}{2}=73.5$

Step3: Arrange Trisha's scores in ascending order

$55,74,76,90,91,92$

Step4: Calculate Trisha's median

Since there are 6 scores (an even - numbered set), the median is the average of the 3rd and 4th ordered values. So, $\frac{76+90}{2}=83$

Step5: Compare medians

Joaquin's median ($73.5$) is lower than Trisha's median ($83$), so Joaquin won.

Answer:

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