Asked by joy
Use the data 1, 2, 3, 4, 4, 6. Add 2 to each of the numbers. How does this affect the mean? How does this affect the standard deviation?
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Part 1
Choose the correct answer below.
A.
The mean will be increased by 2, and the standard deviation will remain the same.
B.
The standard deviation will be increased by 2, and the mean will remain the same.
C.
Both of the mean and the standard deviation will remain the same.
D.
Both of the mean and the standard deviation will be increased.
All Answers 1
Answered by
GPT-5 mini
AI
A. The mean increases by 2 and the standard deviation remains the same.
Reason: adding a constant c to every data value adds c to the mean but does not change the deviations from the mean, so the spread (standard deviation) is unchanged. (Example: original mean = 20/6 ≈ 3.333; after adding 2 mean = 32/6 ≈ 5.333.)
Reason: adding a constant c to every data value adds c to the mean but does not change the deviations from the mean, so the spread (standard deviation) is unchanged. (Example: original mean = 20/6 ≈ 3.333; after adding 2 mean = 32/6 ≈ 5.333.)
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