| Trial | Measurement | Notes |
|---|---|---|
| 1 | 2.01 | Baseline reading |
| 2 | 1.98 | Small negative fluctuation |
| 3 | 2.03 | Near mean |
| 4 | 2.00 | Near mean |
| 5 | 2.08 | Positive tail event |
| 6 | 2.12 | Positive tail event |
Population skewness is
Sample moment skewness uses sample mean and sample spread:
Adjusted skewness reduces small-sample bias:
In frequency mode, sums are weighted by the provided frequencies.
- Choose an input method: a simple list or a value-frequency table.
- Select the skewness definition that matches your report or standard.
- Paste values from experiments, simulations, or instrument logs.
- Press Compute Skewness to view results above the form.
- Check mean, spread, and Pearson coefficient for consistency.
- Download CSV for lab notes, or PDF for sharing and archiving.
1) Why skewness matters in measurements
Many lab signals are not perfectly symmetric. Drift, saturation, and intermittent interference can create long tails in the error distribution. Skewness summarizes that asymmetry, helping you judge whether the mean reflects typical behavior or rare events. In calibration studies, it flags systematic error modes that shift one tail.
2) Interpreting sign and magnitude
Positive skewness indicates a longer right tail: occasional high spikes above the mean. Negative skewness indicates a longer left tail: dropouts or clipping toward lower values. As a guide, |skew| < 0.5 is mild, 0.5–1 moderate, and > 1 strong asymmetry.
3) Choosing a definition: γ1, g1, or G1
This calculator provides population skewness (γ1), the sample moment form (g1), and the adjusted Fisher–Pearson estimator (G1). For finite datasets used to infer a broader process, G1 is often preferred because it reduces small-sample bias.
4) Frequency tables and binned data
In counting experiments and histogram outputs, you may only have bin centers with counts. The value–frequency mode treats counts as weights, reproducing central moments without expanding the dataset. This is efficient when counts are large and keeps calculations stable. Use bin centers and integer counts from your histogram export.
5) Uncertainty and the standard error
Skewness is noisy for small n. A common approximation for its standard error is √(6n(n−1)/((n−2)(n+1)(n+3))). As n grows, uncertainty falls roughly like 1/√n. If skewness is comparable to its error, treat the sign as tentative and collect more data.
6) Robust cross-check: Pearson’s coefficient
Pearson’s second coefficient, 3(x̄ − median)/s, uses the median to reduce sensitivity to extremes. When Pearson’s coefficient and moment-based skewness agree on sign, tail direction is more credible. Disagreement can indicate outliers, truncation, or mixed regimes.
7) Typical sources of skew in physics data
Right-skew appears when rare bursts add energy: photon pile-up, cosmic rays in imaging, impulsive acoustic noise, or switching events. Left-skew can arise from dead-time losses, thresholding, or sensor floor effects. Logging gain and temperature helps explain changes across runs.
8) Reporting best practices
Report n and the skewness definition used. Include mean, median, and standard deviation, and document preprocessing such as clipping, background subtraction, or filtering. Export CSV for lab notes and PDF for sharing to keep results consistent and auditable.
1) What does a skewness value of 0 mean?
A value near 0 suggests the distribution is approximately symmetric around the mean. Small deviations can still occur from noise, limited sample size, or mild outliers.
2) Which skewness definition should I report?
For most experimental datasets treated as samples, use the adjusted estimator (G1) to reduce small-sample bias. Use population skewness only when your dataset represents the full population of interest.
3) Why do I need at least three data points?
Skewness depends on the third central moment and a stable estimate of spread. With fewer than three points, the estimator is not meaningful and can become numerically unstable.
4) Can I compute skewness from a histogram?
Yes. Enter bin centers as values and bin counts as frequencies. This weighted approach reproduces central moments without expanding every count into repeated samples.
5) How do outliers affect skewness?
Outliers can strongly change skewness because cubing deviations amplifies extremes. Compare with Pearson’s coefficient and inspect the raw data to decide whether outliers are physical events or artifacts.
6) What if the standard deviation is zero?
If all values are identical, the spread is zero and skewness is undefined in a strict sense. The calculator will return 0 for moment ratios, but you should interpret it as “no variability,” not a shape statement.
7) Is skewness a substitute for plotting the data?
No. Skewness is a compact summary, but it cannot reveal multimodal structure or time-dependent drift. Use it alongside histograms, time series, and residual checks for robust conclusions.