How was the problem created?
I was reading answer of this question where the author remarked that
The 3rd quartile (Q3) is positioned at .675 SD (std deviation, sigma) for a normal distribution.
I understand that Q3 can be positioned at 0.675 SD during normally distribution. However, I really do not understand how it is at 0.675 SD? Why not at 0.775 SD?
Then, how did I try to find an answer?
I have searched in Google using different keywords.
Here, I found that
It is readily calculated that for the standard normal distribution the first quartile is -.67 (using .2514 for .25) and the third quartile is .67. This means that for normally distributed data, one-half of the data is within 2/3 of a standard deviation unit of the mean.
Here, I also found that they have used 0.675 SD to calculate first and third quartile.
I have also checked these questions (1, 2) to find the answer. However, still I did not find know how Q3 is positioned at 0.675 SD in case of normally distributed data?
Any kind of help will be greatly appreciated.