about 95 % of data with a normal distribution is within one standard deviation of the mean.
what percent of data with a normal distribution is within one standard deviation of the mean?
about 95 %
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in general, 'normal' refers to a lack of significant deviation from the average. the word normal is used in a more narrow sense in mathematics, where a normal distribution describes a population whose characteristics centers around the average or the norm. when looking at a specific behaviour, such as the frequency of lying, a researcher may use a gaussian bell curve to plot all reactions, and a normal reaction would be within one standard deviation, or the most average 68.3%. however, this mathematical model only holds for one particular trait at a time, since, for example, the probability of a single individual being within one standard deviation for 36 independent variables would be one in a million. in statistics, normal is often arbitrarily considered anything that falls within about 1.96 standard deviations of the mean, or the most average 95% (see 1.96). the probability of an individual being within 1.96 standard deviations for 269 independent variables is approximately one in a million. for only 59 independent variables, the probability is just under 5%. under this definition of normal, it is abnormal to be normal for 59 independent variables.
normality (behavior)