Question 1141014: Hello,
I would appreciate it very much if someone could help me with this problem.
Is a measure of 26 inches "far away" from a mean of 16 inches? As someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data.
(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 inches?
(b) Is 26 inches far away from a mean of 16 inches?
(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 inches?
Thank you SO much!
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! (a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 inches?
It is five standard deviations away. This is because 26 inches is 10 inches away from 16 inches, and 10 divided by 2 (which is one standard deviation) is 5.
(b) Is 26 inches far away from a mean of 16 inches?
With a standard deviation of 2, it is VERY far away. (See above...FIVE standard deviations away.) Less than 0.1% of all values would be expected to exceed 26 inches.
(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 inches?
With a standard deviation of 8 inches, a value of 26 inches is 1.25 standard deviations away. (26 inches is 10 inches away from 16 inches, and 10 divided by 8 is 1.25.)
With a standard deviation of 8, about 10% of values would be expected to exceed 26 inches. Furthermore, with a standard deviation of 8, about 80% of the values would be expected to fall between 6 and 26 inches.
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