Question

Statistics:A professor has recorded grades for 10 students but one of the grades is no longer readable. if the mean score on the exam was 82 and the mean of the nine readable scores is 86 …what is the value of the unreadable score?

Answer 1

Given:

a.) The mean score on the exam was 82.

B.) The mean of the nine readable scores is 86.

If the mean score is the average score of all 10 students, therefore:

`\text{ Mean score = }82\text{ = }\frac{\text{ Sum of all scores}}{\text{ 10}}`

The sum of all scores includes the score of the one no longer readable:

`\text{ Sum of all scores = 9 readable scores + 1 unreadable score}`
`\text{ Mean of nine readable scores = 86 = }\frac{\text{ Sum of 9 readable scores}}{9}`

Therefore,

`\text{ 10 x Total mean score = (1 x unreadable score) + (9 x mean of readable scores)}`
`\text{ 10 x 82 = unreadable score + (9 x 86)}`
`\text{ 820 = unreadable score + }774`
`\text{ 820 - 774 = unreadable score}`
`\text{ unreadable score = }46`

Therefore, the unreadable score is 46.