To find the mean of the recorded exam scores, we first need to sum all the scores and then divide by the number of scores. Here's the process:

Step 1: List the exam scores.

The recorded exam scores are: 82, 1, 13, 93, 40, 92, 36, 50, 71, 9, 58, 91, 45, 76, 99

Step 2: Count the total number of scores.

There are 15 scores.

Step 3: Calculate the sum of all the scores.

$82 + 1 + 13 + 93 + 40 + 92 + 36 + 50 + 71 + 9 + 58 + 91 + 45 + 76 + 99 = 856$

Step 4: Calculate the mean.

$\text{Mean} = \frac{\text{Sum of scores}}{\text{Number of scores}} = \frac{856}{15} \approx 57.1$

Thus, the mean score is 57.1 (rounded to one decimal place).

Would you like more details, or do you have any questions?

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Here are 5 related questions:

1. How do you find the median score of this data set?
2. What is the mode of the given exam scores?
3. How would the mean change if one additional score of 100 was added?
4. What is the range of the recorded exam scores?
5. How do you calculate the standard deviation for this data set?

Tip: The mean is sensitive to outliers; large or small values can significantly affect the result.