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 7 inches. Is 26 inches far away from a mean of 16 inches?
Accepted Solution
A:
Answer: Hello!In a normal distribution, between the mean and the mean plus the standar deviation, there is a 34.1% of the data set, between the mean plus the standar deviation, and the mean between two times the standard deviation, there is a 16.2% of the data set, and so on.If our mean is 16 inches, and the measure is 26 inches, then the difference is 10 inches between them.a) if the standar deviation is 2 inches, then you are 10/2 = 5 standar deviations from the mean.b) yes, is really far away from the mean, in a normal distribution a displacement of 5 standar deviations has a very small probability.c) Now the standar deviation is 7, so now 26 is in the range between 1 standar deviation and 2 standar deviations away from the mean.Then this you have a 16% of the data, then in this case, 26 inches is not far away from the mean.