Repeat
Independent result under declared repeatability conditions.
Unit Converters
Density Precision Calculator
Analyze same-condition density repeats without confusing repeatability with accuracy. Every record is retained after unit normalization and the statistics are calculated from unrounded values.
Density repeatability study
Separate repeat scatter from accuracy and total uncertainty
Convert same-condition repeated density measurements to one unit and calculate mean, sample standard deviation, RSD, range, and Type A uncertainty of the mean.
Accepted repeats—
Mean density—
Sample standard deviation—
Relative standard deviation—
Type A uncertainty of mean—
Observed range—
Separate repeat scatter from accuracy and total uncertainty ledgerUnrounded values drive calculations and decisions
| Repeat | Source value | Converted density | Deviation from mean |
|---|
How to use
Separate repeat scatter from accuracy and total uncertainty
Convert same-condition repeated density measurements to one unit and calculate mean, sample standard deviation, RSD, range, and Type A uncertainty of the mean.
- Use repeats from one sample state, method, instrument setup, and temperature.
- Paste at least two positive measurements and preserve their original order.
- Select the source and reporting units before interpreting dispersion.
- Investigate transcription errors or method-defined outliers outside this page.
- Report precision statistics separately from reference bias and calibration uncertainty.
Repeatability quantities
Arithmetic mean
Center of accepted repeated values.
Sample standard deviation
Scatter estimate using n−1 degrees of freedom.
RSD
Standard deviation divided by the absolute mean.
Type A uncertainty
Standard uncertainty of the mean estimated as s/√n.
Result interpretation
Read scatter without calling it accuracy
A small RSD indicates close repeats relative to the mean, not agreement with a certified value. Type A uncertainty becomes smaller as repeat count grows under stable conditions, but systematic effects, temperature bias, calibration, and sample inhomogeneity remain outside this statistic.
Calculation method
Calculate repeatability statistics
Parse every numeric record, reject non-positive or malformed entries, convert through kg/m³, calculate the unrounded mean, use the n−1 sample variance, divide s by |mean| for RSD, divide s by √n for Type A uncertainty, and preserve each row deviation.
Evidence checks
Replicate and unit checks
Repeatability conditions
Operator, instrument, method, time interval, temperature, and sample handling should meet the intended repeatability definition.
Temperature stability
A drifting bath can create real density change that appears as instrument imprecision.
Sample homogeneity
Settling solids, bubbles, or evaporation can make sequential readings represent different measurands.
Outlier governance
Do not delete an inconvenient value automatically; apply the documented method and retain exclusions with reasons.
Resolution effects
Repeated identical digits may reflect display resolution rather than negligible underlying scatter.
Accuracy boundary
Comparison with a certified reference and bias correction require separate evidence.
Uncertainty budget
Type A is one component; include calibration, temperature, buoyancy, repeatability design, and reference values where applicable.
Visual explanation
Repeat-density strip with mean and standard-deviation band
Each repeat remains an individual marker. A center line shows the mean and a band shows one sample standard deviation, so clustering and time order remain visible instead of collapsing into one card.
Detailed calculation process
Mean, sample spread, RSD, and Type A uncertainty
ρ̄ = Σρi/n; s = sqrt(Σ(ρi − ρ̄)²/(n − 1)); RSD = 100s/|ρ̄|; uA(ρ̄) = s/√n
| Symbol | Meaning | Required unit |
|---|---|---|
| ρi | converted repeat | target density unit |
| n | accepted repeat count | count |
| ρ̄ | arithmetic mean | target density unit |
| s | sample standard deviation | target density unit |
| RSD | relative scatter | % |
| uA | Type A standard uncertainty of mean | target density unit |
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Reconciliation:Waiting for current inputs.
Defaults and assumptions
Same-condition repeat measurements
The default series is a compact demonstration near 850 kg/m³. It is not a repeatability limit or a certified data set.
| Check | Current value A | Current value B | Decision role |
|---|
Decision analysis
Use precision evidence in a measurement plan
Use the output to describe observed repeat scatter and plan follow-up. Do not declare a method precise enough until the governing repeatability requirement, sample design, and uncertainty budget are compared.
Examine the ordered residual pattern before accepting a single standard deviation as the complete precision story. Alternating values can indicate digital resolution, a monotonic sequence can indicate thermal drift or settling, and clusters can reveal separate preparation states. Plot or review the records in acquisition order and compare the observed behavior with the method’s repeatability conditions. If an outlier rule is authorized, apply it to the original measurements, document the statistic and critical value, and retain both included and excluded results; never delete a row merely to improve RSD. Consider whether repeated readings are genuinely independent: rereading the same filled cell or stable instrument display may understate preparation and sampling variability. For a reported mean, combine Type A uncertainty with calibration, reference-material, temperature, resolution, buoyancy, and other justified components under the laboratory method. Compare the resulting expanded uncertainty with the decision requirement separately. A low calculated Type A value cannot compensate for a biased instrument, changing sample, or unsuitable method. Precision acceptance should therefore name the governing limit, degrees of freedom, repeat design, and whether individual results or the mean is the intended measurand.
Evidence and data lineage
Retain ordered repeats and instrument context
Retain every raw reading, sequence, unit, temperature, instrument, operator, sample preparation, accepted exclusions, calculation version, and unrounded statistics.
Limits and exclusions
What repeatability does not establish
The page does not test normality, detect drift, calculate reproducibility, correct bias, apply an outlier test, or build a complete measurement uncertainty budget.
Reliable sources
References for Separate repeat scatter from accuracy and total uncertainty
Precision-study terms
Worked cases
Density repeatability decisions
Digital densimeter check
Six stable-temperature repeats show low scatter, then a certified reference is used separately to assess bias.
Slurry sequence
A downward trend across repeats suggests settling; the team changes mixing and sampling rather than reporting one pooled SD.
Important note
Separate repeat scatter from accuracy and total uncertainty: scope before action
Precision cannot establish accuracy. A tightly clustered set may still be wrong by a common systematic amount.
Separate repeat scatter from accuracy and total uncertainty FAQ
Why require at least two values?
Sample standard deviation is undefined with only one observation.
Why use n−1?
It estimates population scatter from a sample whose mean was also estimated.
Can I mix units in one list?
No. Convert or separate the records before entry.
Does low RSD mean accurate density?
No. Accuracy requires reference evidence and bias assessment.
Why preserve order?
Order can reveal drift, settling, warming, or carryover.
Are blank tokens treated as zero?
No. Separators without numbers do not create artificial records.
Can I delete an outlier?
Only under the governing documented rule, with the exclusion retained.
What does Type A include?
Only the statistical contribution estimated from these repeats.
Does more repetition remove systematic error?
No. Repetition reduces mean scatter but not common bias.
Can I compare two laboratories?
Not with repeatability alone; use a reproducibility design.
What unit is RSD reported in?
RSD is dimensionless and displayed as percent.
Why can range look large while SD is modest?
Range depends strongly on extremes and repeat count.
Does rounding affect the statistics?
The page uses unrounded converted values internally.
When is the mean unsuitable?
When the sample state changes or the sequence is not one stable population.