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  • The mean of a set of 110 observations is 55. It was later discovered that three observations, 60, 62, and 65, were incorrectly recorded as 40, 42, and 45. What is the correct mean?<div class='q

The mean of a set of 110 observations is 55. It was later discovered that three observations, 60, 62, and 65, were incorrectly recorded as 40, 42, and 45. What is the correct mean?

Option: 1

53.8


Option: 2

54.4


Option: 3

54.9


Option: 4

55.6


Answers (1)

best_answer

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

The sum of the original 110 observations is 55 \times 110 = 6050.

We need to subtract the incorrect values (40, 42, and 45) and add the correct values (60, 62, and 65) to the sum.

Corrected sum = (6050 - 40 - 42 - 45) + 60 + 62 + 65 = 6050 - 40 - 42 - 45 + 60 + 62 + 65 = 6120.

The correct mean is the corrected sum divided by the number of observations (110).

Corrected mean = 6120 / 110 = 55.63636363636363.

Therefore, the correct mean is approximately 55.63636363636363.

Among the given options,  55.6 is the closest to the correct mean.

 

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