Question

The mean score of 15 students was 82.0. (a) Another student joins, and the mean becomes 82.5. What is the new student's score? (b) Suppose instead that two students join, taking the average from 82 to 83. What could their scores be, if they are restricted to be integer (i.e. whole) numbers? (Give all the possible solutions, under the assumption that the maximum score for an individual student is 100.)

Answer 1

Answer:

a) The new student's score is 90.

b) Their scores are a pair of scores lower than 100 with a mean of 90.5.

Step-by-step explanation:

The mean is the sum of all scores divided by the number of students.

The mean score of 15 students was 82.0

This means that there are 15 students and the sum of the scores is 15*82 = 1230.

(a) Another student joins, and the mean becomes 82.5. What is the new student's score?

Now there are 16 students, the sum of the scores is 1230 + x and the mean is 82.5. So

$82.5 = \frac{1230 + x}{16}$

$1230 + x = 16*82.5$

$x = 1320 - 1230$

$x = 90$

The new student's score is 90.

(b) Suppose instead that two students join, taking the average from 82 to 83. What could their scores be, if they are restricted to be integer (i.e. whole) numbers?

Now there are 2 new students, so 17 in total. The mean score of the new students is 2x. The total score of the class is 1230 + 2x and the mean is 83. So

$83 = \frac{1230 + 2x}{17}$

$1230 + 2x = 1411$

$2x = 181$

$x = 90.5$

The mean of the two students scores is 90.5.

So their scores are a pair of scores lower than 100 with a mean of 90.5.