The average of a collection of 20 measurements was calculated to be 56 cm. But later it was found that a mistake had occurred in one of the measurements which was recorded as 64 cm., but should have been 61 cm. The correct average must be
Options:
A . 54.5 cm
B . 53 cm
C . 56.15 cm
D . 55.85 cm
Answer: Option D Answer: (d)Total length of 20 measurements = 56 × 20 = 1120 cm Correct length of 20 measurements = 1120 – 64 + 61 = 1117 Correct average = $1117/20$ = 55.85 cm 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 = 20, m = 56 a = 61, b = 64 Correct Average = m +${\text"(a-b)"}/ \text"n"n$ = 56 +$({61-64}/20)$= 56 -$3/20$= 56 – 0.15 = 55.85 cm
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