•Degree of scatter (measure of central tendency) of population is quantified by calculating the standard deviation

•Std. dev. of population = s

•Std. dev. of sample = s

 

•Characterize sample by calculating

Standard deviation and the normal distribution

  •Standard deviation defines the shape of the normal distribution (particularly width) 

•Larger std. dev. means more scatter about the mean, worse precision.

 

•Smaller std. dev. means less scatter about the mean, better precision.

•There is a well-defined relationship between the std. dev. of a population and the normal distribution of the population: 

•m ± 1s encompasses 68.3 % of measurements 

•m ± 2s encompasses 95.5% of measurements 

•m ± 3s encompasses 99.7% of measurements 

•(May also consider these percentages of area under the curve)