The mean of 50 numbers is 30. Later it was discovered that two entries were wrongly entered as 82 and 13 instead of 28 and 31. Find the correct mean.
Options:
A .  30.66
B .  36.12
C .  38.21
D .  29.28
Answer: Option D Answer: (d)Required average = 30+${(28+31-82-13)}/50$ = 30 $(-36/50)$= 30 – 0.72 = 29.28 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 = 50, m = 30 a = 28, b = 31 p = 82, q = 13 Correct Average = m + ${\text"(a+b-p-q)"}/ \text"n"n$ = 30 +${(28+31-82-13)}/50$ = 30 +$({59-95}/50)$= 30 -$36/50$= 30 – 0.72 = 29.28
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