https://file.aiquickdraw.com/mathbot/file/1726598879368af9xzes7.jpg

Let's carefully analyze the dot plots and the statements provided to determine which ones are true.

### Observations:
- **Noah's scores** are: 2, 3, 4, 4, 4, 5, 5, 6, 6 (9 scores)
- **Jada's scores** are: 1, 2, 2, 3, 3, 4, 5, 5, 6 (9 scores)

### Statement 1: **Noah’s scores have greater variability than Jada’s scores.**
- Noah’s scores are more clustered around the middle, with more scores concentrated in the range of 4-6, whereas Jada’s scores are spread across a wider range (from 1 to 6).
- **Conclusion**: This statement is **false** because Jada’s scores appear to have greater variability.

### Statement 2: **Noah scored better than Jada on every assignment.**
- Both students have scores in the same range (2-6), and Jada has lower scores at 1 and 2, while Noah has no score lower than 2. However, for some scores, Jada scores the same or better than Noah.
- **Conclusion**: This statement is **false**, as there are some assignments where Jada scored the same or better (e.g., score of 5 or 6).

### Statement 3: **The standard deviation of Noah’s scores is equal to the standard deviation of Jada’s scores.**
- The standard deviation measures the spread of the data. Since Jada’s scores are spread out more (with scores as low as 1 and more variation), and Noah’s scores are more clustered, Jada’s scores likely have a higher standard deviation.
- **Conclusion**: This statement is **false**. Jada’s scores have a higher standard deviation.

### Statement 4: **The mean of Noah’s scores is greater than the mean of Jada’s scores.**
- To verify this, let’s compute the means:
  - Noah’s mean: \((2 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 6) / 9 = 39 / 9 = 4.33\)
  - Jada’s mean: \((1 + 2 + 2 + 3 + 3 + 4 + 5 + 5 + 6) / 9 = 31 / 9 = 3.44\)
- **Conclusion**: This statement is **true**. Noah’s mean score (4.33) is higher than Jada’s (3.44).

### Statement 5: **Using only Noah’s scores, the mean is equal to the median.**
- Noah’s scores: 2, 3, 4, 4, 4, 5, 5, 6, 6
  - Median: Since there are 9 scores, the middle score (5th score) is 4.
  - Mean: \(4.33\) (as calculated earlier).
- **Conclusion**: This statement is **false**, as the mean (4.33) is not equal to the median (4).

### Final Conclusion:
- The only true statement is: **The mean of Noah’s scores is greater than the mean of Jada’s scores.**

Would you like more details on any part of the analysis?

Here are five questions to extend your understanding:
1. How do you calculate standard deviation from the given data?
2. What is the difference between mean and median in terms of data distribution?
3. How can you visually assess variability between two sets of data?
4. What impact does a larger range of data have on the standard deviation?
5. How does the concentration of scores around the mean affect the distribution?

**Tip:** To quickly compare variability between two sets of data, look at the spread of scores (the range and clustering) in a dot plot or histogram.

The dot plots show 9 scores on a 10-question trivia game for two students. Select ALL the statements that must be true.

Analyze the dot plots of Noah and Jada's scores to assess the mean, median, and variability. This problem helps students compare data sets using key statistical measures such as mean, median, and standard deviation.

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