The average marks secured by 36 students was 52. But it was discovered that an item 64 was misread as 46. What is the correct mean of marks ?
Options:
A . 53.5
B . 54
C . 52.5
D . 53
Answer: Option C Answer: (c)Difference of correct and incorrect marks = 64 – 46 = 18 ∴ Correct mean = 52 + $18/36$ = 52.5 Aliter : Using Rule 26,If average of n numbers is m later on it was found that a number 'a’ was misread as 'b’. The correct average will be = m +${\text"(a-b)"}/ \text"n"$.Here, n = 36, m = 52 a = 64, b = 46 New mean = m + ${\text"(a - b)"}/\text"n"$= 52 +${(64 – 46)}/36$ = 52 + $18/36$= 52 + $1/2$ = 52.5
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