Suppose a box and whisker diagram was given with no data of mean and standard deviation.
I am able to find the range of Mean(NOT sure if it is correct) as $\frac{(Xmin+Q1+Q2+Q3)}{4}$$<mean<\frac{(Q1+Q2+Q3+Xmax)}{4}$
where
Q1=first quartile
Q2=median
Q3=third quartile
Since $\frac{Xmin+Q1}{2}$<mean<$\frac{Q3+Xmax}{2}$
The possible location of mean is shown as below:
but I don't know the range of standard deviation.
I know that the more disperse the data is, the higher the standard deviation.
That mean the larger the difference between mean and the data, the higher the standard deviation.But I do not know which quartile the mean is in, so can not find the range of standard deviation.
Can somebody give me some hints?
