91Ó°ÊÓ

First, let's talk about what the mean formula is. The mean, also known as the average, helps us understand the central value of a set of numbers.

To calculate the mean, you simply add up all the numbers (scores, in this case) and then divide by the number of scores. The formula can be written as: \[ \text{Mean} = \frac{\text{Sum of scores}}{\text{Number of scores}}. \]

This formula is the key to solving many statistical problems, including our example problem with the unreadable score.

Next, we need to focus on finding the sum of scores. This is often the first step in calculating an average or solving other related problems.

In our original exercise, we first needed to find the sum of all 20 exam scores. The mean was provided as 82, and there were 20 students. So, the total sum of all scores is calculated as: \[ \text{Sum of all scores} = \text{Mean} \times \text{Number of students} = 82 \times 20 = 1640. \]

It's also crucial to find the sum of the readable scores. Here, we know that the mean of the 19 readable scores is 84. Thus, the sum of the 19 readable scores can be calculated as: \[ \text{Sum of 19 readable scores} = 84 \times 19 = 1596. \]

These sums allow us to proceed with finding the unreadable score.

Finally, after finding the sums, let's move on to the average score calculation part.

We have already found the sum of all scores and the sum of the 19 readable scores. The unreadable score can be determined by subtracting the sum of the readable scores from the total sum.

Mathematically, it looks like this: \[ \text{Unreadable score} = \text{Sum of all scores} - \text{Sum of 19 readable scores} = 1640 - 1596 = 44. \]

So, by using the mean formula and understanding the sum of the scores, we arrived at the unreadable score of 44. This approach can be applied to many similar problems involving averages and sums.