Question

Statistics: a professor recorded 10 exam grades but one of the grades is not readable. if the mean score on the exam was 82 and the mean of the 9 readable scores is 84 what is the value of the unreadable score?

Answer 1

To mean of a set is given by the sum of all values in the data-set divided by the number of values.

We have that the mean of the whole set is 82.

The mean of the 9 readable scores is 84.

So:

`\begin{gathered} (x)/(9)=84 \\ x=84\cdot9 \\ x=756 \end{gathered}`

So, we 9 readable scores add up to 801. If we add 756 to a number, y, and divide by 10, we'll have the mean score of the exam, 82.

`\begin{gathered} (756+y)/(10)=82 \\ 756+y=820 \\ y=820-756 \\ y=64 \end{gathered}`

So, the grade of the unreadable score was 64.