To determine which score is more likely for the new student, we should analyze the given data and use measures like the mode, mean, and median to identify a central tendency in the existing scores.

The quiz scores are: $11, 17, 10, 9, 13, 11, 11, 17, 16, 15, 19$

1. Mode:

The mode is the most frequent score. In this case, the score of 11 appears 3 times, making it the mode.

2. Mean:

The mean (average) score is calculated by summing the scores and dividing by the number of scores: $\text{Mean} = \frac{11 + 17 + 10 + 9 + 13 + 11 + 11 + 17 + 16 + 15 + 19}{11} = \frac{149}{11} \approx 13.55$

3. Median:

To find the median, we first order the scores: $9, 10, 11, 11, 11, 13, 15, 16, 17, 17, 19$ The median is the middle score, which in this case is 13 (6th value).

Conclusion:

• The mode is 11.
• The mean is about 13.55, so scores near 12–14 are common.
• The median is 13, indicating that central scores tend to cluster around this value.

Analyzing the given options:

• 9 is close to a low existing score but is less frequent.
• 12 is very close to both the mean and median, making it a likely score.
• 7 is lower than any current score.
• 20 is higher than any current score.

Most likely score: 12, since it's close to the central tendency (mean and median).

Would you like further details or have any questions?

Here are five related questions for deeper understanding:

1. How would the analysis change if the scores were out of 100 instead of 20?
2. What is the impact of outliers on the mean and median?
3. How can we calculate the probability of a new student scoring exactly 12?
4. How does the mode influence the likelihood of a new score?
5. How could you use a frequency distribution to visualize the scores?

Tip: The median is often more robust than the mean when dealing with outliers or skewed data.