Is a measure of 25 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 3 inches. How many standard deviations is 25 inches from 16 inches? (b) Is 25 inches far away from a mean of 16 inches? (c) Suppose the standard deviation of the underlying data is 7 inches. Is 25 inches far away from a mean of 16 inches?

a) 25 is 3 standard deviation from the mean

b) Is far away from the mean, only 0,3 % away from the right tail

c) 25 is pretty close to the mean (just a little farther from 1 standard deviation)

Step-by-step explanation:

We have a Normal Distribution with mean 16 in.

Case a) we also have a standard deviation of 3 inches

3 * 3 = 9

16 (the mean) plus 3*σ equal 25 in. the evaluated value, then the value is 3 standard deviation from the mean

Case b) 25 is in the range of 99,7 % of all value, we can say that value is far away from the mean, considering that is only 0,3 % away from the right tail

Case c) If the standard deviation is 7 then

mean + 1*σ = 16 + 7 = 23

25> 23

25 is pretty close to the mean only something more than 1 standard deviation