A professor has recorded exam grades for 19 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 72 and the mean of the 18 readable scores is 73, what is the value of the unreadable score? 

To find the value of the unreadable score, we can use the concept of the mean and the relationship between the total sum of the scores and the number of students.

### Step-by-step solution:

1. **Let the unreadable score be \( x \).**
2. The mean of the 19 students' scores is given as 72. Therefore, the total sum of all 19 scores can be expressed as:
   \[
   \frac{\text{Sum of all 19 scores}}{19} = 72
   \]
   Hence, the sum of all 19 scores is:
   \[
   \text{Sum of all 19 scores} = 72 \times 19 = 1368
   \]

3. The mean of the 18 readable scores is given as 73. Therefore, the total sum of the 18 readable scores is:
   \[
   \frac{\text{Sum of 18 readable scores}}{18} = 73
   \]
   Hence, the sum of the 18 readable scores is:
   \[
   \text{Sum of 18 readable scores} = 73 \times 18 = 1314
   \]

4. Now, we know that the sum of all 19 scores is the sum of the 18 readable scores plus the unreadable score \( x \). Therefore:
   \[
   1368 = 1314 + x
   \]

5. Solving for \( x \):
   \[
   x = 1368 - 1314 = 54
   \]

### Conclusion:
The value of the unreadable score is \( \boxed{54} \).

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Would you like to go through more examples related to averages or have any questions on this one?

Here are some related questions:
1. How would the result change if the mean of the 18 readable scores was different?
2. What is the relationship between the mean and the sum of the values in a set of numbers?
3. How would you approach a problem where multiple unreadable scores are missing?
4. What happens to the mean when an extremely high or low score is added to a dataset?
5. How can you calculate the sum of scores if the mean and number of students are known?

Tip: When dealing with averages, remember that the total sum of the numbers is always the mean multiplied by the number of elements. This is a quick way to reverse-engineer a problem when certain information is missing.

A professor has recorded exam grades for 19 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 72 and the mean of the 18 readable scores is 73, what is the value of the unreadable score?

Learn how to solve for an unreadable exam score when given the mean of the total and partial data. This problem involves calculating the sum of values using the mean and algebra. Suitable for students in Grades 7-9.

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