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  • The mean and standard deviation of the weights of 200 objects were found to be 50 kg and 8 kg, respectively. Later, it was discovered that a weight of 50 kg was wrongly recorded as 55 kg. What are

The mean and standard deviation of the weights of 200 objects were found to be 50 kg and 8 kg, respectively. Later, it was discovered that a weight of 50 kg was wrongly recorded as 55 kg. What are the correct mean and standard deviation, respectively?

 

Option: 1

50 kg and 8 kg


Option: 2

49 kg and 8 kg


Option: 3

50 kg and 7 kg


Option: 4

49 kg and 7 kg


Answers (1)

best_answer

To find the correct mean and standard deviation, we need to adjust the wrongly recorded weight and recalculate these statistics.

First, let's adjust the weight of 55 kg to the correct weight of 50 kg.

The sum of the original 200 weights is 50 kg \times 200 = 10,000 kg.

We need to subtract the wrongly recorded weight (55 kg) and add the correct weight (50 kg) to the sum.

Corrected sum = (10,000 kg - 55 kg) + 50 kg = 10,000 kg - 55 kg + 50 kg = 9,995 kg.

The correct mean is the corrected sum divided by the number of objects (200).

Corrected mean = 9,995 kg / 200 = 49.975 kg.

Next, let's adjust the standard deviation. Since we only changed one weight, the impact on the standard deviation is minimal.

The corrected standard deviation remains the same as the original standard deviation, which is 8 kg.

Therefore, the correct mean is approximately 49.975 kg, and the correct standard deviation is 8 kg.

Among the given options, 49 kg and 8 kg is the closest to the correct mean and standard deviation.

 

Posted by

rishi.raj

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