A set of test papers was machine scored. Later it was discovered that two points should be added to each score. Student A said, "The mean score should

Jaden Easton

Jaden Easton

Answered question

2021-02-23

A set of test papers was machine scored. Later it was discovered that two points should be added to each score. Student A said, "The mean score should also be increased by two points." Student B added, "The standard deviation should also be increased by two points." Who is right? Justify your answer.

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-02-24Added 117 answers

Given: Two points need to be added to each score
When you add two points to each score, then the mean will be adjusted in the same way (as the mean measures the center of the scores) and thus the mean needs to be increased by two points.
When you add two points to each score, then the standard deviation will be unaffected (as the standard deviation mensures the spread of the scores and the spread of the scores is unaffected when all scores increase by the same amount). Thus the standard deviation should not be changed.
This then implies that Student A is correct as only the mean needs to be increased by twu polite:
Student A is correct.

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