Let's analyze the answers based on the image you provided.

1. Question 1: Standard Deviation refers to:

   • Your answer is: A (The distance between the highest score and the lowest score)
   • Correct answer: B (Most common measure of the spread of scores)
     • Explanation: Standard deviation measures the dispersion or spread of data points relative to their mean, not just the distance between the highest and lowest scores.

2. Question 2: What is the range of the set of scores 11, 51, 51, 91?

   • Your answer is: A (80)
   • Correct answer: A (80)
     • Explanation: The range is the difference between the highest and lowest values in the set. $91 - 11 = 80$, so your answer is correct.

3. Question 3: In a P.E. class, there are 25 freshmen, 30 sophomores, and 10 juniors. If the freshmen averaged 89, the sophomores averaged 85, and the juniors averaged 82, what is the mean grade of the entire class?

   • Your answer is: B (85.08)
   • Let's calculate to check the answer.

Calculation for the mean:

To find the mean, we need to calculate the total score of the entire class and divide by the total number of students.

• Freshmen: $25 \times 89 = 2225$
• Sophomores: $30 \times 85 = 2550$
• Juniors: $10 \times 82 = 820$

Total score = $2225 + 2550 + 820 = 5595$

Total number of students = $25 + 30 + 10 = 65$

Mean = $\frac{5595}{65} = 86.08$

• Correct answer: A (86.08)

Conclusion:

1. Incorrect, the correct answer is B.
2. Correct.
3. Incorrect, the correct answer is A.

Would you like more details on any of these? Here are 5 questions related to this:

1. What is the formula for standard deviation?
2. How can you find the variance of a data set?
3. What is the difference between range and standard deviation?
4. Can the standard deviation be zero? If so, when?
5. How would changing one score in the data set affect the mean and standard deviation?

Tip: Always ensure to check whether a question is asking for spread (standard deviation) or extreme values (range), as they measure different aspects of a data set.