Is a measure of 22 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.

Question

Is a measure of 22 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 22 inches from 16 inches?

​(b) Is 22 inches far away from a mean of 16 ​inches?

​(c) Suppose the standard deviation of the underlying data is 4

inches. Is 22 inches far away from a mean of 16 inches?

Answer 1

a) (22-16)/2 = 8/2 = 4 standard deviations from the mean

b) in most statistical uses, more than 2 or 3 is considered too far to be random, and enough to reject a null hypothesis. but in some physics they go by "six signma" or 6 standard deviations frome the mean to be too "far away"

c) (22-16)/4 = 8/4 = 2 standard deviations from the mean. It's borderline "too far way" for most problems

It's too far away if you're using a 90% confidence interval, which is common. borderline if 95%, not too far away if using 99%

an alternative measure of "too far away" is calculating an "outlier" which is too far from most of the data to be reliable, a suspect datum that may be a mistake, recorded incorrectly or a fluke of some kind. for that you need the IQR and Q1 and Q3, the 25th and 75th percentiles and the median. IQR is the interquartile range