Statistics

Shipping

statistics

Reduce signal to six scalar measures: mean, std, min, max, rms, median

Signature

Inputs

signalSignalrequired

Outputs

meanScalar
stdScalar
minScalar
maxScalar
rmsScalar
medianScalar

Description

Statistics collapses an entire input signal into six scalar summary measures, emitted on independent output ports: mean, std, min, max, rms, and median. It is a pure reduction over all $N$ samples currently present on the input, computing each statistic in a single pass (with median requiring an internal sort). Every output is a Scalar, not a signal.

The node is stateless: outputs depend only on the current input buffer, with no running accumulator carried across evaluations. Feeding it a windowed or framed stream therefore yields per-frame statistics; feeding it a complete captured buffer yields whole-record statistics.

All six measures inherit the physical unit of the input samples: mean, std, min, max, rms, and median of a quantity in volts are themselves in volts (variance-like quantities are square-rooted back to the base unit, so the unit is preserved rather than squared). Uncertainty ( $σ$ ) propagates into mean — averaging $N$ independent samples reduces the standard error by $N$ — while order statistics (min, max, median) carry the $σ$ of the selected sample.

Note that std uses the sample standard deviation and is a population/sample dispersion measure, distinct from the input's per-sample measurement uncertainty $σ$ ; the two describe different things and should not be conflated.

Mathematics

\overset{x}{ˉ} = \frac{1}{N} i = 1 \sum N x_{i}, x_{rms} = \frac{1}{N} i = 1 \sum N x_{i}^{2}

s = \frac{1}{N - 1} i = 1 \sum N (x_{i} - \overset{x}{ˉ})^{2}

x_{m i n} = i min x_{i}, x_{m a x} = i max x_{i}, \tilde{x} = median_{i} x_{i}

Examples

Characterizing a noisy sensor buffer

Wire a captured accelerometer channel (unit $m/ s^{2}$ ) into signal. The node reports mean (DC offset / bias), std (dispersion), rms (total signal power including DC), and min/max (peak excursions). Because $x_{rms}^{2} = \overset{x}{ˉ}^{2} + s_{pop}^{2}$ , comparing rms against mean reveals how much energy is AC versus DC.

Robust vs. mean level

For a signal with occasional spikes, read both mean and median from the same node. A large gap mean - median flags skew or outliers, since the median is insensitive to a few extreme samples while the mean is dragged toward them.

signal -> statistics.mean   -> sink   # outlier-sensitive
signal -> statistics.median -> sink   # robust center

Applications

Signal quality metrics in test benches: extracting DC bias (mean), noise floor (std), and crest information (max/rms) from a captured waveform.
RMS-based power and amplitude measurement for AC electrical signals, vibration, and acoustics.
Automated pass/fail limit checking, feeding min/max/mean scalars into a comparator against specification thresholds.
Outlier and skew detection by comparing the robust median against the mean of the same buffer.

Neat

The identity $x_{\mathrm{rms}}^2 = \bar{x}^2 + s_{\text{pop}}^2$ ties the three moment-based outputs together: RMS is the quadrature sum of the DC (mean) and AC (population std) components, so any two determine the third.

Because every output is a Scalar rather than a signal, the node acts as a bridge from the streaming/time domain into scalar dashboards, comparators, and limit logic without a separate sampler.

Known issues

`std` uses the $N-1$ (sample) denominator and is therefore undefined for a single-sample input; with $N=1$ the dispersion collapses to zero or NaN depending on the buffer.

For an even number of samples the `median` is the average of the two central order statistics, which for integer-valued or bimodal data can produce a value that never occurs in the input.