Question

One of my classes had 12 students. The scores on a test were 36, 62, 75, 75, 86, 89,

90, 90, 94, 98. The missing scores are the same. If there average of all of the scores
was 80.25, find the missing scores.

Answer 1

Answer: The missing scores are both 84.

Explanation:

To find the missing scores, you can use the formula for the average:

`\[\text{Average} = \frac{\text{Sum of all scores}}{\text{Total number of students}}\]`

You're told that the average of all the scores was 80.25 and that there are 12 students in the class. Therefore, the sum of all the scores can be calculated as:

`\[\text{Sum of all scores} = \text{Average} * \text{Total number of students} = 80.25 * 12 = 963\]`

Next, you'll want to find the sum of the given scores:

`\[36 + 62 + 75 + 75 + 86 + 89 + 90 + 90 + 94 + 98 = 795\]`

Now, you can find the sum of the missing scores:

`\[\text{Sum of missing scores} = \text{Sum of all scores} - \text{Sum of given scores} = 963 - 795 = 168\]`

You're told that the missing scores are the same. Since there are 2 missing scores, each missing score would be:

`\[\text{Each missing score} = (168)/(2) = 84\]`

So, the missing scores are both 84.