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  • The mean and standard deviation of the test scores of 200 students were found to be 75 and 10, respectively. Later, it was discovered that a score of 75 was wrongly recorded as 80. What are the cor

The mean and standard deviation of the test scores of 200 students were found to be 75 and 10, respectively. Later, it was discovered that a score of 75 was wrongly recorded as 80. What are the correct mean and standard deviation, respectively?

 

Option: 1

75 and 10


Option: 2

74 and 10


Option: 3

75 and 9


Option: 4

74 and 9


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 80 to the correct score of 75.

The sum of the original 200 scores is 75 \times 200 = 15,000.

We need to subtract the wrongly recorded score (80) and add the correct score (75) to the sum.

Corrected sum = (15,000 - 80) + 75 = 15,000 - 80 + 75 = 14,995.

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

Corrected mean = 14,995 / 200 = 74.975.

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 10.

Therefore, the correct mean is approximately 74.975, and the correct standard deviation is 10.

Among the given options, 74 and 10 is the closest to the correct mean and standard deviation.




 

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