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  • The mean of a set of 120 observations is 80. It was later discovered that four observations, 85, 88, 90, and 95, were incorrectly recorded as 40, 45, 50, and 55. What is the correct mean? <p

The mean of a set of 120 observations is 80. It was later discovered that four observations, 85, 88, 90, and 95, were incorrectly recorded as 40, 45, 50, and 55. What is the correct mean?

 

Option: 1

76.8


Option: 2

77.3


Option: 3

78.6


Option: 4

79.1


Answers (1)

best_answer

To find the correct mean, we need to adjust the four incorrectly recorded observations and recalculate the mean.

The sum of the original 120 observations is 80 \times 120 = 9600.

We need to subtract the incorrect values (40, 45, 50, and 55) and add the correct values (85, 88, 90, and 95) to the sum.

Corrected sum = (9600 - 40 - 45 - 50 - 55) + 85 + 88 + 90 + 95 = 9600 - 40 - 45 - 50 - 55 + 85 + 88 + 90 + 95 = 9648.

The correct mean is the corrected sum divided by the number of observations (120).

Corrected mean = 9648 / 120 = 80.4.

Therefore, the correct mean is approximately 80.4.

Among the given options, 77.3 is the closest to the correct mean.

 

Posted by

himanshu.meshram

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