SPREAD / TRANSPARENT METHOD
From deviations to spread: choose your denominator and inspect the calculation.
Predefined synthetic data only. The link shares the example, never your numbers or metadata. Loading an example replaces current fields.
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Uses the columns and decimal format selected above. Row numbers refer to the parsed table including the header; completely blank rows may already have been ignored. No correction or exclusion is automatic.
At most 80 notices are displayed; every row is checked.
The report retains the original table, edits and excluded rows. It contains data: share deliberately. This is an editable local trail, not a certification.
Select up to 8 numeric columns. Every selected cell must be valid; no individual missing values are removed. This is a descriptive comparison, not a test between groups.
Open a .json file exported by StatNivo. Replaces current data and recalculates in this calculator; nothing is uploaded.
Raw data: up to 10,000 values per series.
Temporary storage is off unless you select the option.
Undefined values: empty cells. No additional rounding in CSV files. CSV headings use stable English identifiers for software compatibility.
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LOOK BEYOND THE MEAN
Scroll the chart horizontally to read the full scale. Frequencies are also available in the table.
50 rows per page. Original row positions are retained; CSV includes all observations.
UNDERSTAND, DON’T JUST CALCULATE
Positive and negative deviations from the mean cancel in a sum. Squaring avoids this cancellation and gives large deviations more weight. To return to the original units, take the square root of variance: that is standard deviation.
For 10, 12, 14, the mean is 12. Deviations are −2, 0, 2 and their squares add to 8. Population variance is 8/3 ≈ 2.66667; sample variance is 8/2 = 4. These are different denominators, not different rounding of the same calculation.
Values in volts produce a variance in volts squared. Raw variances are not directly comparable across different units or scales. The n − 1 correction concerns sample variance estimation under the usual sampling assumptions; it cannot fix biased data collection.
For 2, 4, 4, 4, 5, 5, 7, 9 the population SD is 2; sample SD is √(32/7) ≈ 2.13809. Choose the population formula when describing the full population of interest, not because the number is smaller.
Standard deviation describes the spread of observations. The usual standard error of the mean is sample SD / √n under independent sampling with finite variance. For sample SD 10 and n = 25, SEM = 2. Repeated dependent readings do not automatically count as 25 independent measurements.
Paste the entire table, select its real delimiter and header, then preview it. In decimal-comma data, use a semicolon or tab as the column delimiter. If Y is missing in row 3, fix that row rather than moving row 4 up.