To find the mean of the reading scores, we sum all the scores and then divide by the number of students.

The scores are: $77, 77, 13, 88, 13, 88, 88, 14, 13, 14, 15, 15$

Step-by-step Calculation:

1. Sum of the scores:

$77 + 77 + 13 + 88 + 13 + 88 + 88 + 14 + 13 + 14 + 15 + 15$

2. Perform the addition:

$77 + 77 = 154$ $154 + 13 = 167$ $167 + 88 = 255$ $255 + 13 = 268$ $268 + 88 = 356$ $356 + 88 = 444$ $444 + 14 = 458$ $458 + 13 = 471$ $471 + 14 = 485$ $485 + 15 = 500$ $500 + 15 = 515$

The total sum of the scores is $515$.

3. Number of students: $n = 12$

4. Calculate the mean: $\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Students}}$ $\text{Mean} = \frac{515}{12}$

5. Perform the division: $\text{Mean} \approx 42.92$

The mean of the reading scores is: $\boxed{42.92}$

Would you like more details or have any questions?

Here are 8 related questions to expand on this information:

1. How do you find the median of a data set?
2. What is the range of the reading scores in this data set?
3. How do you calculate the mode of a data set?
4. What is the significance of having multiple modes in a data set?
5. How does the presence of extreme values affect the mean?
6. What other measures of dispersion can be used to describe data variability?
7. How can the mean be used to interpret the overall performance of students?
8. What is the difference between the sample mean and the population mean?

Tip: When dealing with data sets that contain repeated values, be sure to count each value accurately to avoid errors in your calculations.