In manufacturing it is useful to have a quick estimate of the standard deviation. This is often done with the range rule of thumb: σ ~ (sample range)/4. This rule works well when the data comes from a normal distribution and the sample size is around 30, but fails miserably for other distributions and sample sizes. Through the use of Monte Carlo simulations we suggest new rules of thumb for the normal distribution, uniform distribution, and exponential distribution which are dependent on sample size. We then seek to verify these empirical results theoretically.

Author Bio

Alfredo Ramirez is currently a graduate student at Tennessee Technological University and is pursuing a Masters in Mathematics. He graduated from the University of Tennessee at Martin with a Bachelor of Science in Mathematics. His primary field of study is in statistics and is working a thesis pertaining to the Pareto distribution along side Dr. David Smith.

Charles Cox is currently a senior at the University of Tennessee at Martin. He is majoring in Secondary Education-Mathematics Concentration with dreams and hopes of becoming a high school teacher in the state of Tennessee. Helping students succeed in mathematics is his overall inspiration and goal in life, and with a little self-induced studying of the abstractness of the subject being his hobby