Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

Values

Required list. Observations in time order.

Alpha

Optional number. Smoothing weight for the newest observation; higher values react faster.

The cited overview of Statistics supplies background for the terminology and domain context used by this tool.^[1]

Compute an exponential moving average series seeded with the first observation. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Average

Returned list. EMA series of the same length, starting at the first value.

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• Alpha must be at least 0.
• Alpha must be no greater than 1.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

• Moving Average

  Smooth a series into arithmetic means over overlapping fixed-size windows.

• Autocorrelation Calculator

  Compute sample autocorrelation coefficients for lags one through a maximum lag.

• Benford's Law First-Digit Checker

  Count leading nonzero decimal digits 1–9 in nonzero observations for comparison with Benford's logarithmic proportions. A small or range-restricted sample alone is not evidence of fraud.