Let’s analyze the problem in the image. The dot plots show scores for Noah and Jada in a trivia game. We are asked to determine which of the provided statements must be true.

1. Noah’s and Jada’s Scores:
   • Noah’s scores: 1, 2, 3, 4, 5, 6, 7 (with a higher concentration of scores in the middle and spread over the whole range).
   • Jada’s scores: 2, 3, 4, 5, 6 (with several scores clustered around 3, 4, and 5, and no scores below 2 or above 6).

Evaluating Each Statement:

• (A) "Noah’s scores have greater variability than Jada’s scores."

  • True. Noah’s scores range from 1 to 7, while Jada’s range is narrower, from 2 to 6. This indicates that Noah’s scores have more variability.

• (B) "The standard deviation of Noah’s scores is equal to the standard deviation of Jada’s scores."

  • False. Noah’s scores are more spread out, while Jada’s scores are clustered, meaning Noah’s standard deviation is larger.

• (C) "The mean of Noah’s scores is greater than the mean of Jada’s scores."

  • True. Noah’s scores include 6s and 7s, which are larger than Jada’s highest scores, indicating Noah’s mean should be higher.

• (D) "Noah scored better than Jada on every assignment."

  • False. Jada has scores of 3, 4, and 5, while Noah has some lower scores like 1 and 2. So, Noah didn’t always score better.

• (E) "Using only Noah’s scores, the mean is equal to the median."

  • True. Noah’s scores are symmetric (1 to 7), making the mean and median both 4.

True Statements:

• A, C, E are true based on the data provided.

Would you like further details on any of these calculations or explanations?

Related Questions:

1. How do we calculate the mean and median for a dataset?
2. What is the significance of standard deviation in measuring variability?
3. How can we visually compare the variability between two datasets?
4. What methods are used to compare the means of two different datasets?
5. How does the symmetry of a dataset affect its mean and median?

Tip:

When comparing two datasets, always check the range and distribution (shape) of the data to understand variability and central tendencies like the mean and median.