Let's solve these questions one by one.

Question 1

We need to find the average of the numbers: 15, 15, 19, and 27.

To calculate the average:

1. Add the numbers: $15 + 15 + 19 + 27 = 76$
2. Divide the sum by the count of numbers, which is 4: $\text{Average} = \frac{76}{4} = 19$

So, the average of the numbers is 19.

Question 2

We need to find the mean quiz score based on the table values: 20, 19, 15, and 13.

To calculate the mean:

1. Add the scores: $20 + 19 + 15 + 13 = 67$
2. Divide by the total number of quizzes, which is 4: $\text{Mean score} = \frac{67}{4} = 16.75$

Thus, the mean quiz score is 16.75.

Would you like further explanation on these calculations or have any other questions?

Here are some related questions to further explore:

1. What is the median of the numbers 15, 15, 19, and 27?
2. How would the average change if another number, say 30, were added to the set in Question 1?
3. What is the difference between mean, median, and mode?
4. How can the range of scores in Question 2 be calculated?
5. What impact does an outlier have on the mean score?

Tip: Remember, the average (or mean) is sensitive to extreme values (outliers), which can skew the result, especially in smaller data sets.