Can someone please explain standard deviations?

Question

Lets say the mean = 42.5

Standard Deviation = 6.8

Can you gauge the lowest and highest score from here, and how many percentage of cases are at the higher or lower end?

Many many thanks!

Answer 1

High = 49.3

Low = 35.7

Cool thought, 3,000 miles per oil change, This is most likely the lower standard deviation, we probably could go much longer with out changing the oil.  

Answer 2

Although you cannot definitively determine the range (i.e., the lowest and highest score in a distribution) given only the mean and the SD, you can determine the approximate percentage of cases in a given range AROUND the mean - assuming that your distribution is normal (approximates the normal, Gussian curve).

In the case you mentioned, you will want to use the 68-95-99 "empirical rule". This means that 68% of the cases will fall within 1 SD of the mean (i.e., 42.5 + and minus  6.8), 95% of the cases will fall within 2 SD of the mean (i.e., 42.5 + and minus 13.6), and 99% of cases will fall within 3 SD of the mean (i.e., 42.5 plus/minus 20.4).

~M~

Answer 3

I think the standard deviation is just a term that means what would be a deviation from the mean which would not be exceptional. I don't think you can find out the percentage of cases at the higher or lower end. I guess try Wikipedia