The problem presents a dot plot showing 9 scores from two students, Noah and Jada, on a 10-question trivia game. We're tasked with determining which statements about the scores are true.

Let's analyze each statement based on the dot plots.

1. Statement A: "Noah's scores have greater variability than Jada's scores."

   • Variability refers to the spread of the data. Noah's scores are spread out more, ranging from 2 to 7, while Jada's scores range from 3 to 7. Since Noah's scores include more spread, this statement appears true.

2. Statement B: "The standard deviation of Noah's scores is equal to the standard deviation of Jada's scores."

   • Standard deviation measures variability. Since Noah’s scores have a wider range than Jada’s, it’s unlikely that the standard deviations are equal. Therefore, this statement is false.

3. Statement C: "The mean of Noah's scores is greater than the mean of Jada's scores."

   • Noah's scores are generally higher than Jada's, as Noah has more scores in the upper range (5, 6, and 7), while Jada's are more spread out across the middle (4, 5, and 6). This suggests that the mean of Noah’s scores might be slightly higher. This statement could be true upon calculation.

4. Statement D: "Noah scored better than Jada on every assignment."

   • From the plot, there are instances where Jada and Noah have the same scores, such as both scoring 4 and 5. Also, Jada's lowest score is 3, while Noah's lowest score is 2. Hence, Noah did not score better in every instance. This statement is false.

5. Statement E: "Using only Noah's scores, the mean is equal to the median."

   • The median is the middle value of the ordered data. For Noah's scores, arranging them gives us: 2, 2, 3, 4, 5, 5, 6, 6, 7. The median is the 5th value, which is 5. To check if the mean equals the median:
     • The sum of Noah's scores is $2 + 2 + 3 + 4 + 5 + 5 + 6 + 6 + 7 = 40$.
     • The mean is $\frac{40}{9} \approx 4.44$, which is not equal to 5. This statement is false.

Final Answers:

• A: True
• B: False
• C: Likely True
• D: False
• E: False

Would you like any further details or clarification on any of the points?

5 Related Questions:

1. How is standard deviation calculated, and why does it reflect variability in the data?
2. What is the difference between mean, median, and mode, and why are they useful in statistics?
3. How can you visually assess data variability from a dot plot?
4. What impact does an outlier have on the mean and median of a dataset?
5. How do you calculate the range of a dataset, and what does it tell you about data spread?

Tip:

When comparing variability between two datasets, always check the range and dispersion of data points visually and use statistical measures like variance or standard deviation for more precision.