Live math canvas
Variance Calculator: 16.5 sample variance. population variance 13.2 · mean 9 · squared-difference total 66 across 5 values
Formula applied
CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.
Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).Your live breakdown
These values come from the controls above and update when the calculator changes.
Resulting answer
population variance 13.2 · mean 9 · squared-difference total 66 across 5 values
Assumptions used
Use population variance for a complete group; use sample variance for an estimate from a sample.
Master’s Tip
Master’s Tip: print the mean, squared-difference total and denominator choice beside the answer. Most variance mistakes are denominator mistakes or value-inclusion mistakes, not arithmetic mysteries.
Printable record
Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.
Direct answer
For 4, 7, 9, 10 and 15, the mean is 9. The squared-difference total is 66, giving population variance 13.2 and sample variance 16.5. This calculator keeps both denominators visible so classroom, lab and spreadsheet checks are easier to audit.
Variance: 16.5 sample variance
This pre-calculated state lets readers and answer engines verify what the tool returns before the inputs change.Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).
The default inputs, formula and result stay together so the number can be checked or quoted without losing context.Copy the default solved state as Markdown or CSV, then print the page for a clean formula and result record.
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Copy this prompt with your final CalculationTime result when you want a second-pass explanation, comparison or next-step checklist.
Use this CalculationTime result as the source: Variance Calculator. Default output: Variance = 16.5 sample variance. Formula/method: Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).. Explain the result, state the assumptions, and suggest the next calculation to check.Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).
For 4, 7, 9, 10 and 15, the mean is 45 ÷ 5 = 9. Squared differences are 25, 4, 0, 1 and 36, for a total of 66. Population variance is 66 ÷ 5 = 13.2. Sample variance is 66 ÷ 4 = 16.5.
Master’s Tip: print the mean, squared-difference total and denominator choice beside the answer. Most variance mistakes are denominator mistakes or value-inclusion mistakes, not arithmetic mysteries.
Standard or basis: descriptive-statistics arithmetic for population and sample variance. The page follows the common n and n − 1 denominator distinction used in statistics teaching and data summaries; no curriculum, scientific or regulatory standard is claimed.
Methodology & Accuracy
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).
Standard or basis: descriptive-statistics arithmetic for population and sample variance. The page follows the common n and n − 1 denominator distinction used in statistics teaching and data summaries; no curriculum, scientific or regulatory standard is claimed.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master’s Tip: print the mean, squared-difference total and denominator choice beside the answer. Most variance mistakes are denominator mistakes or value-inclusion mistakes, not arithmetic mysteries.
Knowledge check
Use these quick checks to confirm that the result, formula and assumptions make sense before you reuse the number.
The default result starts with Value 1, Value 2, Value 3. The current pre-solved output is variance = 16.5 sample variance.
The proof is in the formula, worked example and assumptions sections. Together they show the arithmetic, the default state and the limits of the result.
Use the related calculators, printable record or source notes to check the next practical step instead of treating one output as the end of the workflow.
Accuracy feedback
This lightweight check records your answer in this browser only. It does not send personal data and does not claim a live backend review queue.
Find the mean, subtract the mean from each value, square those differences, add them, divide by the correct denominator, and keep the result in squared units.
Population variance divides by n when the values are the whole group. Sample variance divides by n − 1 when the values are a sample used to estimate a larger population.
No. Variance is the average squared difference from the mean. Standard deviation is the square root of variance, which returns the spread to the original unit scale.
Yes. If every included value is the same, every difference from the mean is zero, so both population and sample variance are zero.
Variance squares each difference from the mean, so its unit is squared. If the data is in metres, variance is in square metres; standard deviation returns to metres.
Variance is a measure of spread around the mean. It is useful when a data record needs the squared-difference audit trail before taking the square root for standard deviation.
Each included value is compared with the mean. The differences are squared so negative and positive deviations do not cancel each other out, and larger deviations carry more weight.
Population variance describes the exact group entered. Sample variance estimates a wider population from a smaller set, so the denominator changes from n to n − 1.
A variance answer is easiest to trust when the report keeps the included values, mean, squared-difference total, denominator and result together. That is useful for homework, lab notes, quality checks and spreadsheet verification.