MEAN ESTIMATION / TRANSPARENT METHOD
Estimate the mean and its uncertainty margin using the t distribution.
Predefined synthetic data only. The link shares the example, never your numbers or metadata. Loading an example replaces current fields.
Choose options explicitly. Missing cells are flagged, not skipped.
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.
Temporary storage is off unless you select the option. Optional sessionStorage, off by default. Keeps text, table and settings across tools and languages in this tab. Browser session restoration can retain it. Use “Delete saved data” on a shared device. Nothing is uploaded.
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
The t method assumes independent observations from appropriate sampling. It is exact under normality; large samples may allow an approximation, but strong skew, extreme values or dependence can invalidate it. These assumptions are not tested; systematic errors and instrument calibration are not measured.
The confidence level describes method coverage over repeated samples. It is not the probability that the true mean lies in this computed interval, nor an interval containing that percentage of individual observations.
For observations 1, 2, 3: mean = 2, s = 1, n = 3. At 95%, t ≈ 4.302653; the margin is about 2.484138 and the interval [−0.484138, 4.484138]. This demonstrates the formula; it does not validate its assumptions.
Summary mode: no observations, quartiles or data charts have been fabricated.
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.