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? (

Question

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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.)

Mathematics

1 answer:

Leona [9.2K] · Answer 1 · 2026-03-22T09:18:56+03:00

Answer:

a) The score of the new student is 90.

b) Their scores consist of two values less than 100 that average to 90.5.

Step-by-step explanation:

The mean is calculated by dividing the total of all scores by the number of students.

For the 15 students, the average score was 82.0

This implies that there are 15 students whose score sum totals 15*82 = 1230.

(a) An additional student comes in, changing the mean to 82.5. What is the score of the new student?

Now with 16 students, the total score amounts to 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) If two students join, raising the average to 83. What could their scores be while ensuring they are whole numbers?

With 2 additional students, there are now 17 in total. The average score of the new students is 2x. The overall class score would then be 1230 + 2x with a mean of 83. Thus

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

$1230 + 2x = 1411$

$2x = 181$

$x = 90.5$

The average of the two students’ scores is 90.5.

Thus, their scores must be two values under 100 with an average of 90.5.