Question

The mean s recorded by 27 candidates happened to be 64%. During inspection it was found that one candidate actually scored 74% s instead of 47% recorded in the result sheet. What will be the correct mean?

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Answer 1

Explanation:

the mean score is the sum of all scores divided by the number of scores.

64 = (s1+s2+s3+...+s26+s27)/27

64×27 = (s1+s2+s3+...+s26+s27)

1728 = (s1+s2+s3+...+s26+s27)

now, one of the scores changes from 47 to 74. that means the sum of all scores is increased by 74-47 = 27.

so, we get

1728 + 27 = (s1+s2+s3+...+s26+s27+27)

1755 = (s1+s2+s3+...+s26+s27+ 27)

we still have 27 scores, so for the updated mean we have to divide both sides by 27 again :

1755/27 = (s1+s2+s3+...+s26+s27+27)/27

65 = (s1+s2+s3+...+s26+s27+27)/27

the correct mean is therefore 65%.