Question

bernice received the following scores on five science tests: 96, 77, 86, 97, and 89. which of the following statements is true? the median of the set of scores is 86. the mode of the set of scores is 96. the mean and the median of the set of scores are the same. the mean of the set is less than the median.

Explanation:

First, let's list the scores: 96, 77, 86, 97, 89. We need to sort them in ascending order: 77, 86, 89, 96, 97.

Step 1: Find the median

The median is the middle value of a sorted list. Since there are 5 values (odd number), the median is the 3rd value. So the median is 89? Wait, no, wait. Wait, sorted list: 77, 86, 89, 96, 97. The 3rd value is 89? Wait, no, wait, let's check again. Wait, 77 (1st), 86 (2nd), 89 (3rd), 96 (4th), 97 (5th). So median is 89. Wait, but the first option says median is 86, which is wrong.

Step 2: Find the mode

The mode is the most frequently occurring value. All scores appear once, so there is no mode (or all are modes, but 96 appears once, so the statement "the mode is 96" is wrong because 96 only appears once, same as others.

Step 3: Calculate the mean

The mean is the sum of the scores divided by the number of scores. Sum = 77 + 86 + 89 + 96 + 97. Let's calculate that: 77 + 86 = 163; 163 + 89 = 252; 252 + 96 = 348; 348 + 97 = 445. Number of scores is 5. So mean = 445 / 5 = 89. Wait, median is 89, so mean and median are the same? Wait, the third option says "The mean and the median of the set of scores are the same." Let's check again.

Wait, sorted list: 77, 86, 89, 96, 97. Median is 89 (3rd term). Mean: (77 + 86 + 89 + 96 + 97)/5 = (77 + 86 = 163; 163 + 89 = 252; 252 + 96 = 348; 348 + 97 = 445) 445 / 5 = 89. So mean is 89, median is 89. So the third option (The mean and the median of the set of scores are the same) is correct. Wait, the options are:

1. The median of the set of scores is 86. (Wrong, median is 89)
2. The mode of the set of scores is 96. (Wrong, no mode or all are modes, but 96 only once)
3. The mean and the median of the set of scores are the same. (Correct, both 89)
4. The mean of the set is less than the median. (Wrong, mean is 89, median is 89, so mean is not less than median)

So the correct statement is "The mean and the median of the set of scores are the same."

Answer:

The mean and the median of the set of scores are the same.