Named for its characteristic shape, the bell curve is a graph of the “normal distribution” (i.e. most common) or Gaussian distribution of the probability of finding a value of a given variable. The graph shows that data are “clustered” near to the mean, with a sharp drop-off and long tail on either side.
Two parameters control the position and “wideness” of the normal distribution:
- The mean
- The standard deviation
i.e. for a normal distribution, 68% of observed values are within 1 standard deviation; 95% are within two and 99.7% within three standard deviations.
However, real data rarely follows a perfectly normal distribution: it is usually either skewed assymetrically on either side of the mean (“skewness”), or shows “fatter or thinner tails” (higher or lower “kurtosis”) than the normal (kurtosis=3).