Math Problem Statement

Two classes were given identical quizzes.

Class A had a mean score of 8.3 and a standard deviation of 0.4 Class B had a mean score of 8.5 and a standard deviation of 0.8

Which class scored better on average? Select an answer Class A Class B

Which class had more consistent scores? Select an answer Class A Class B

Solution

  1. Which class scored better on average?
    Answer: Class B
    Explanation: Class B has a higher mean score (8.5) compared to Class A's mean score (8.3), indicating that on average, Class B performed better.

  2. Which class had more consistent scores?
    Answer: Class A
    Explanation: Consistency in scores is indicated by a lower standard deviation. Class A has a standard deviation of 0.4, which is lower than Class B's standard deviation of 0.8, meaning Class A's scores were more consistent.

Would you like more details on these answers or have further questions?


Here are five additional related questions for practice:

  1. If Class A’s mean score was increased by 0.3, how would the mean scores of both classes compare?
  2. What is the probability that a randomly selected student from Class A scored above the mean of Class B?
  3. If a new student scored 9 in both classes, how would that affect the standard deviation of each class?
  4. What percentage of students in Class B scored within one standard deviation of the mean?
  5. If the quiz is out of 10, what percentage of students in Class A likely scored below 8?

Tip: The standard deviation is a measure of variability, and a smaller standard deviation means data points are closer to the mean, indicating more consistency.

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Standard Deviation

Formulas

Mean = (Sum of scores) / (Number of scores)
Standard Deviation = sqrt((Sum of (Score - Mean)^2) / (Number of scores))

Theorems

Properties of Mean and Standard Deviation

Suitable Grade Level

Grades 9-10