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  • The mean of a set of 90 observations is 85. It was later discovered that three observations, 90, 92, and 95, were incorrectly recorded as 80, 82, and 85. What is the correct mean?  <

The mean of a set of 90 observations is 85. It was later discovered that three observations, 90, 92, and 95, were incorrectly recorded as 80, 82, and 85. What is the correct mean?

 

Option: 1

83.8


Option: 2

84.4


Option: 3

84.9


Option: 4

85.6


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 90 observations is 85 \times 90 = 7650.

We need to subtract the incorrect values (80, 82, and 85) and add the correct values (90, 92, and 95) to the sum.

Corrected sum = (7650 - 80 - 82 - 85) + 90 + 92 + 95 = 7650 - 80 - 82 - 85 + 90 + 92 + 95 = 7690.

The correct mean is the corrected sum divided by the number of observations (90).

Corrected mean = 7690 / 90 = 85.44444444444444.

Therefore, the correct mean is approximately 85.44444444444444.

Among the given options, 84.4 is the closest to the correct mean

 

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Gaurav

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