Calculate Population / Sample Standard Deviation, full step derivation, confidence intervals, frequency table & data distribution chart.
This statistical calculator fully replicates and extends the calculation display format of the reference screenshot, supports population & sample two calculation modes, outputs complete step-by-step derivation formulas, confidence interval visual error bars, frequency tables and data distribution charts.
| Control Name | Function Definition | Usage Example |
|---|---|---|
| Population Standard Deviation Radio | Full dataset is entire population; variance divided by N, symbol σ | Use when all target objects are measured in input data |
| Sample Standard Deviation Radio | Data is random partial sample; variance divided by N-1 to eliminate bias, symbol s | For small random sampling subsets of total population |
| Data Input Textarea | Accept numeric data, auto split commas/spaces/newlines; filter invalid letters/symbols | Input: 10, 12 23\n16 → clean array [10,12,23,16] |
| Calculate All Statistics Button | Trigger parsing, full formula computation, render all results, formulas, tables & chart | After entering data, click to generate full statistical report |
| Clear All Button | Empty input box, hide all preview and result panels, reset page state | One-click clear all input data and calculation results |
| Load Demo Sample Data Button | Auto fill the standard test dataset from reference screenshot for fast demonstration | Auto fill: 10, 12, 23, 23, 16, 23, 21, 16 |
| Cleaned Dataset Preview Block | Show filtered valid numeric values, prompt discarded non-numeric content | Remind users which input content cannot be parsed as numbers |
,, space character, line break new lineStandard deviation (σ = population, s = sample) quantifies the dispersion degree of a dataset. Small value = data concentrated near average; large value = wide data fluctuation range.
σ = √[ (1/N) × Σ(xᵢ − μ)² ]
σ² = Σ(xᵢ − μ)² / N
Calculation Demo (Sample Dataset 10,12,23,23,16,23,21,16):
μ = (10+12+23+23+16+23+21+16) / 8 = 144 / 8 = 18
σ² = [(10-18)² + (12-18)² + ... + (16-18)²] / 8 = 192 / 8 = 24
σ = √24 ≈ 4.8989794855664
s = √[ (1/(N-1)) × Σ(xᵢ − x̄)² ]
s² = Σ(xᵢ − x̄)² / (N − 1)
Note: Sample deviation has obvious statistical bias when dataset size N < 10, results are only for reference.
SEM = σ / √N
SEM represents the standard deviation of the sample mean distribution, used to calculate margin of error for different confidence levels (68.3% ~ 99.9999%). Z-score corresponding to each confidence level is multiplied with SEM to get final margin of error.
Calculate standard deviation of product size, weight, performance indicators. If measured data exceeds the mean ± standard deviation normal range, adjust production process to stabilize product consistency.
Compare temperature standard deviation of coastal and inland regions. Coastal cities have low temperature deviation (stable climate); inland areas show high deviation with drastic temperature swings.
Standard deviation of asset return rate quantifies investment volatility risk. Two assets with identical average return: higher SD = larger profit/loss fluctuation, higher investment risk.
Analyze exam score dispersion, questionnaire survey data volatility, judge whether experimental group data has stable distribution or extreme outlier values.
Cause: Input text only contains empty spaces, letters, symbols with no recognizable numbers.
Solution: Clear input box and re-enter numeric values separated by commas/spaces.
Cause: Less than two valid numbers selected under sample mode (denominator N-1 becomes zero, undefined division).
Solution: Input more than one value or switch to population mode for single data entry.
Cause: Input text includes non-numeric characters such as letters, emoji, special punctuation marks.
Solution: Delete irrelevant text content, only retain numbers and standard separators.
Cause: All data points in dataset are identical, standard deviation equals zero with no data dispersion.