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Emily, a teacher, was calculating the test scores of her class, which consisted of 50 students. Initially, she calculated the class average to be 75. However, upon inspection, she discovered that scores 90 and 65 were mistakenly noted as 80 and 60. What is the correct class average (up to one decimal place) after rectifying these mistakes?

Question

Emily, a teacher, was calculating the test scores of her class, which consisted of 50 students. Initially, she calculated the class average to be 75. However, upon inspection, she discovered that scores 90 and 65 were mistakenly noted as 80 and 60. What is the correct class average (up to one decimal place) after rectifying these mistakes?

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Solution

Step 1: Calculate the total score Emily initially calculated. This is done by multiplying the initial average by the number of students. So, 75 (average score) * 50 (number of students) = 3750.

Step 2: Correct the mistakes in the scores. The score of 90 was initially noted as 80, so we add the difference to the total score. Similarly, the score of 65 was initially noted as 60, so we also add this difference. So, 3750 (initial total score) + 10 (difference in first score) + 5 (difference in second score) = 3765.

Step 3: Calculate the correct average by dividing the corrected total score by the number of students. So, 3765 (corrected total score) / 50 (number of students) = 75.3.

Therefore, the correct class average, after rectifying the mistakes, is 75.3.

This problem has been solved

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