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  • The mean of a set of 70 observations is 120. It was later discovered that four observations, 130, 135, 140, and 145, were incorrectly recorded as 95, 100, 105, and 110. What is the correct mean?</p

The mean of a set of 70 observations is 120. It was later discovered that four observations, 130, 135, 140, and 145, were incorrectly recorded as 95, 100, 105, and 110. What is the correct mean?

 

Option: 1

118.6


Option: 2

119.2


Option: 3

119.9


Option: 4

120.5


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 70 observations is 120 \times 70 = 8400.

We need to subtract the incorrect values (95, 100, 105, and 110) and add the correct values (130, 135, 140, and 145) to the sum.

Corrected sum = (8400 - 95 - 100 - 105 - 110) + 130 + 135 + 140 + 145 = 8400 - 95 - 100 - 105 - 110 + 130 + 135 + 140 + 145 = 8550.

The correct mean is the corrected sum divided by the number of observations (70).

Corrected mean = 8550 / 70 = 122.14285714285714.

Therefore, the correct mean is approximately 122.14285714285714.

Among the given options, 119.9 is the closest to the correct mean.

 

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