The average of marks of 14 student was calculated as 71. But it was later found that the marks of one student had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32. The correct average is :
Options:
A . 68
B . 67
C . 71
D . 69
Answer: Option D Answer: (d)According to question, Total marks = 71 × 14 = 994 Correct total marks = 994 + (56 – 42) + (32 – 74) = 994 + 14 – 42 = 966 ∴ Required average = $966/14$ = 69 Aliter : Using Rule 27,If the average of n numbers is m later on it was found that two numbers a and b misread as p and q. The correct average = m +${\text"(a+b-p-q)"}/ \text"n"$.Here n = 14, m = 71 a = 56, b = 42 p = 32, q = 74 Correct Average = m +${\text"(a+b-p-q)"}/ \text"n"n$= 71 +${(56+ 32- 42- 74)}/14$= 71 -$28/14$= 71 – 2 = 69
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