Let's analyze the question.

The scores are: 96, 77, 86, 97, 89. We need to determine which of the provided statements is true. To do this, we will calculate the necessary measures of center (mode, mean, median).

Step 1: Mode

The mode is the number that appears most frequently in the data set. In this case, all the scores appear only once, so there is no mode. Thus, the statement "The mode of the set of scores is 96" is false.

Step 2: Mean

The mean is the average of the scores. To calculate it:

$\text{Mean} = \frac{96 + 77 + 86 + 97 + 89}{5} = \frac{445}{5} = 89$

So, the mean is 89.

Step 3: Median

To find the median, we first arrange the scores in ascending order:

$77, 86, 89, 96, 97$

Since there are 5 numbers, the median is the middle number, which is 89.

Step 4: Analyze the statements

• Statement 1: "The mode of the set of scores is 96." — False (no mode exists).
• Statement 2: "The mean of the set is less than the median." — False (mean and median are both 89, so they are equal, not less than).
• Statement 3: "The mean and the median of the set of scores are the same." — True (both are 89).
• Statement 4: "The median of the set of scores is 86." — False (the median is 89, not 86).

Thus, the correct answer is "The mean and the median of the set of scores are the same."

Would you like more details or have any questions?

Related questions:

1. How would the mean and median change if the highest score were removed?
2. How do you find the mode if there is no repeating number?
3. What happens to the median if a sixth number is added to this set?
4. Can a data set have more than one mode?
5. What are other examples where the mean and median are the same?

Tip:

When calculating the mean and median, arranging numbers in order first simplifies finding the median!