Stem and leaf plot Standard deviation question This is a question cropped out of a midterm practice exam. It states to calculate the standard deviation but I'm confused because it would take me a significantly long time calculating this under the  exam duration. Is there by any chance a shortcut?

 A: First, you need to realize that the numbers run from a low of  6.0
to a high of 18.2. (Not 60 to 182.) Notice "leaf unit o.1."
The mean seems to be roughly 11.6 and only 5% of the 31 observations
(that is 1 or 2 of them) lie more than about 6 units away from
the mean (that is more than 11.6 + 6 = 17.6, or less than 11.6-6 = 5.6). So by the Empirical Rule the SD might be 3 (and not much
bigger). 
The Empirical Rule (ER) also says that about 2/3 of the
observations (20 or 21) might be between 8.6 and 14.6. The
actual count is about 21. So again the Empirical rule seems
consistent with about an SD of about 3. 
Personally, I think it is stretching the intended accuracy of the ER to
try to distinguish between 3.05 and 3.15. Even so, I would pick 3.05.
--Especially, it it had stars next to it!
(Text examples and questions on exams generally tend to give
the ER more credit for accuracy than is really the case in practice.)
Note: There is another possibility. Some textbooks say you can
estimate the SD by dividing the range by 4 (or some say 5).
In your case it happens that the range is 12.2, and dividing
by 4 gives exactly 3.05. (Amazing coincidence!) 
When the sample size is around 25
dividing by 4 sometimes works OK, and when the sample size is
around 100 dividing by 5 sometimes works OK. The actual number
to divide by depends on the sample size. (Such divisors are
printed in some engineering statistics texts.) 
If you
have been taught this rule, go ahead and use it in your
statistics class, but please do not take it seriously if you ever
have any real data to analyze.
