Mean

where N is
the number of data points, i ranges from 1 to N, and x_{i} is each data
point.

Standard Deviation

where N, i, and x_{i} are defined the same as above,
and μ is the mean.

Standard Deviation of the Mean

where N is the number of data points, and σ_{x}
is the standard deviation.

Total error

where σ_{sys} and
σ_{r} are the systematic and
random error, respectively. The standard deviation can be treated as a random
error.

Reduced Chi-Squared

where y_{i,th} is the theoretical value (expected value), y_{i,obs} is the observed value, σ_{i} is the error associated
with the y_{i,obs} value, N is the number of data points,
and ν is the degrees of freedom given as ν = N - *p*, where *p *is the number
of free parameters.