Question

there are 8 sophomores on the academic team. at the last competition, they each took the math test. their scores were 82%, 92%, 76%, 72%, 92%, 74%, 80%, and 78%. what was the median math score of the sophomores?
○ 79%
○ 82%
○ 87%
○ 92%

Explanation:

Step1: Order the scores

First, we need to order the given scores from least to greatest. The scores are 82%, 92%, 76%, 72%, 92%, 74%, 80%, and 78%. When we order them: 72%, 74%, 76%, 78%, 80%, 82%, 92%, 92%.

Step2: Find the median

Since there are 8 scores (an even number), the median is the average of the two middle numbers. The two middle numbers are the 4th and 5th numbers in the ordered list. The 4th number is 78% and the 5th number is 80%? Wait, no, wait. Wait, let's re - order: 72, 74, 76, 78, 80, 82, 92, 92. Wait, 8 numbers. The positions are 1:72, 2:74, 3:76, 4:78, 5:80, 6:82, 7:92, 8:92. Wait, no, that's a mistake. Wait, 8 numbers. The median is the average of the (n/2)th and (n/2 + 1)th terms where n = 8. So n/2=4, n/2 + 1 = 5. So the 4th term is 78, the 5th term is 80? Wait, no, wait the original scores: 82, 92, 76, 72, 92, 74, 80, 78. Let's sort them correctly:

72, 74, 76, 78, 80, 82, 92, 92. Yes, that's correct. Now, the 4th term is 78, the 5th term is 80? Wait, no, wait 72 (1), 74 (2), 76 (3), 78 (4), 80 (5), 82 (6), 92 (7), 92 (8). Wait, no, 8 numbers. So median is average of 4th and 5th. 4th is 78, 5th is 80? Wait, that can't be. Wait, no, I must have made a mistake. Wait the scores are 82, 92, 76, 72, 92, 74, 80, 78. Let's list them:

72, 74, 76, 78, 80, 82, 92, 92. So positions 1 - 8. The median for even n is (n/2 th term + (n/2 + 1)th term)/2. n = 8, so n/2 = 4, n/2 + 1 = 5. So 4th term is 78, 5th term is 80? Wait, but that's not one of the options. Wait, I must have sorted wrong. Wait, 82, 92, 76, 72, 92, 74, 80, 78. Let's re - sort:

72, 74, 76, 78, 80, 82, 92, 92. Wait, 80 is 5th, 82 is 6th? Wait no, 72 (1), 74 (2), 76 (3), 78 (4), 80 (5), 82 (6), 92 (7), 92 (8). Oh! I see my mistake. I thought 80 was 5th, 82 was 6th. So the two middle numbers are the 4th and 5th? Wait no, for n = 8, the median is the average of the (8/2) = 4th and (8/2 + 1)=5th terms. So 4th term: 78, 5th term: 80? But 78 + 80 = 158, divided by 2 is 79. Ah! So the median is 79%.

Answer:

79%