Suppose the average score on a national test is 600, with a standard deviation of 50. If each score is increased by 10, what are the new mean and standard deviation. a. 600, 60 b. 610, 50 c. 610, 55 d. 610, 60 e. 600, 50

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Mathematics

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9 October, 10:00

Suppose the average score on a national test is 600, with a standard deviation of 50. If each score is increased by 10, what are the new mean and standard deviation. a. 600, 60 b. 610, 50 c. 610, 55 d. 610, 60 e. 600, 50

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Ignacio Morgan · Answer 1

b. 610, 50

Step-by-step explanation:

The mean score is the sum of all scores divided by the number of tests.

So if you increase the grade on each test, the mean will increase.

The standard deviation is the square root of the sum of the power of 2 of all scores subtracted by the mean (that is, the distance between each score and the mean) and divided by the number of tests.

As you increase each score by 10, the mean will change by 10. However, the distance between each score and the mean will stay the same, which means that the standard deviations remains unchanged.

In this problem, we have that:

Mean = 600

Standard deviation = 50

Scores increased by 10

So

Mean = 610

Standard deviation = 50

So the correct answer is:

b. 610, 50