in large sets of measurements, all distributions tend to become gaussian (normal) distributions.  the large number is defined as 30. so in experiments with more than 30 repetitions, 68% of the readings will be clustered around the mean, one standard-deviation on either side...

what does this tell us about the experiment ? that you are not the snowflake you thought yourself to be

also, 97 % will be within 4 std-deviations around the mean