Multiple choice

Grades for the test on proofs did not go as well as the teacher had hoped. The mean grade was 68, the median grade was 64, and the standard deviation was 12. The teacher curves the score by raising each score by a total of 7 points. Which of the following statements is true? I. The new mean is 75. II. The new median is 71. III. The new standard deviation is 7.

  1. I only

  2. III only

  3. I and II only

  4. I, II, and III

  5. None of the statements are true
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Adding a constant to every data point increases the mean and median by that constant, but does not change the standard deviation. New mean = 68 + 7 = 75. New median = 64 + 7 = 71. Standard deviation remains 12.

AI explanation

Properties of central tendency state that adding a constant to every score increases the mean and median by that constant, but leaves the standard deviation unchanged. The new mean is 68 + 7 = 75, and the new median is 64 + 7 = 71. The standard deviation remains 12 because adding a constant does not change the spread of the data. Therefore, only statements I and II are true.

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