A class of݊ n pupils takes a spelling test. Their mean score for the test is݉ m. Another pupil takes the test and scores݊ n. When this pupil’s result is included with the other results it is found that the mean has decreased by 2. Which equation below gives the correct expression for݊ n in terms of݉ m?

Answer:

20) D

Number of pupils in first group = n
Mean of first group = m
Total sum of scores for the first group = nm

A new score of another pupil is added.
Total number of pupils now = n + 1
Mean score now = m – 2
Total score now = (n + 1) x (m – 2)

n (m – 2) + 1 (m – 2)
nm – 2n + m – 2         (eq 1)

However, it is mentioned that the student’s score = n
Therefore, total score now = nm + n         (eq 2)

eq 1 = eq 2

nm – 2n + m – 2 = nm + n

m – 2 = nm + n – nm + 2n

m – 2 = n + 2n

m – 2 = 3n

n=  m – 2
          3