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  • The mean and standard deviation of the test scores of 200 students were found to be 60 and 12, respectively. Later, it was discovered that a score of 60 was wrongly recorded as 55. What are the cor

The mean and standard deviation of the test scores of 200 students were found to be 60 and 12, respectively. Later, it was discovered that a score of 60 was wrongly recorded as 55. What are the correct mean and standard deviation, respectively?

Option: 1

60 and 12


Option: 2

61 and 12


Option: 3

60 and 11


Option: 4

61 and 11


Answers (1)

best_answer

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

First, let's adjust the score of 55 to the correct score of 60.

The sum of the original 200 scores is 60 \times 200 = 12,000.

We need to subtract the wrongly recorded score (55) and add the correct score (60) to the sum.

Corrected sum = (12,000 - 55) + 60 = 12,000 - 55 + 60 = 12,005.

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

Corrected mean = 12,005 / 200 = 60.025.

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

The corrected standard deviation remains the same as the original standard deviation, which is 12.

Therefore, the correct mean is approximately 60.025, and the correct standard deviation is 12.

Among the given options,  61 and 12 is the closest to the correct mean and standard deviation.

 

Posted by

Gautam harsolia

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