A professor has recorded exam grades for $30$ students in his class, $1$ of the $30$ grades is unreadable. The mean score on the exam was $82$, and the mean score of the $29$ available scores is $84$,
What is the value of the unreadable score?
A professor has recorded exam grades for $30$ students in his class, $1$ of the $30$ grades is unreadable. The mean score on the exam was $82$, and the mean score of the $29$ available scores is $84$,
What is the value of the unreadable score?
$ 82=\text{mean score}=\frac{\text{sum of all scores}}{30}=\frac{\text{missing score}+\text{sum of all others}}{30}. $ Therefore $ 30\cdot82 = \text{missing score}+\text{sum of all others}. $ $ 30\cdot82=\text{missing score}+\left(29\cdot\text{mean of all others}\right)= \text{missing score}+(29\cdot84). $ So $ 30\cdot82=\text{missing score}+(29\cdot84). $ Can you find the missing score given that?
If our missing person's grade was $84$, the average would be $84$. But the average is $82$. To bring down the average to $82$, the missing person must have received a grade of $(2)(30)$ below $84$.