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Math & Statistics

Variance Calculator

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Math & Statistics

Variance Calculator

Live answer16.5 sample variancepopulation variance 13.2 · mean 9 · squared-difference total 66 across 5 values
Live result16.5 sample variancepopulation variance 13.2 · mean 9 · squared-difference total 66 across 5 values
Formula used

Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).

This is the method behind the answer, so the result can be checked rather than simply trusted.

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Your numbers, formula and explanation together

Variance Calculator: 16.5 sample variance. population variance 13.2 · mean 9 · squared-difference total 66 across 5 values

Formula applied

The exact method behind this answer

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).
  1. Apply the formulaMean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).16.5 sample variancepopulation variance 13.2 · mean 9 · squared-difference total 66 across 5 values

Your live breakdown

Current inputs in the calculation

These values come from the controls above and update when the calculator changes.

Value 1
4
Enter the data values. Use active count to choose how many boxes are included.
Value 2
7
Value 3
9
Value 4
10
Value 5
15
Value 6
0
Value 7
0
How many values to include
5 2 to 7
Use 2 through 7. Later boxes are ignored when the active count is lower.

Resulting answer

16.5 sample variance

population variance 13.2 · mean 9 · squared-difference total 66 across 5 values

Answer
16.5 sample variance
Live support
population variance 13.2 · mean 9 · squared-difference total 66 across 5 values

Assumptions used

What this answer assumes

Use population variance for a complete group; use sample variance for an estimate from a sample.

  • The active count is rounded to a whole number from 2 to 7.
  • Only Value 1 through the active count are included; later boxes are ignored.
  • Population variance divides by n when the entered values are the whole group being described.
  • Sample variance divides by n − 1 when the entered values are a sample used to estimate a wider population.
  • This page uses unweighted numeric values; grouped frequency tables and weighted variance need a separate method.

Master’s Tip

How to use the result well

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

What belongs in the saved calculation

Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.

Value 1
4
Enter the data values. Use active count to choose how many boxes are included.
Value 2
7
Value 3
9
Value 4
10

Visual grid

This number is one point on a larger pattern

Variance is not just a final answer. It is a step on a line: before and after, input and output, assumption and result.

Micro-timehours, minutes, shiftsHuman scaledays, weeks, projectsMacro-timemonths, years, calendars
InputFormulaResult
16.5 sample variance

CalculationTime keeps the path visible: the input, the method and the final number belong together.

CalculationTime

Variance Calculation Report

Report date:

16.5 sample variancepopulation variance 13.2 · mean 9 · squared-difference total 66 across 5 values

Inputs

Value 1
4
Value 2
7
Value 3
9
Value 4
10
Value 5
15
Value 6
0
Value 7
0
How many values to include
5 2 to 7

Method

Mean = sum of values ÷ n. Population variance σ² = Σ(x − mean)² ÷ n. Sample variance s² = Σ(x − mean)² ÷ (n − 1).

  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.

Assumptions

  • The active count is rounded to a whole number from 2 to 7.
  • Only Value 1 through the active count are included; later boxes are ignored.
  • Population variance divides by n when the entered values are the whole group being described.
  • Sample variance divides by n − 1 when the entered values are a sample used to estimate a wider population.

Notes

Use this space on the printed report for client, supplier, classroom, job-location, measurement, quote or approval notes.

Source: https://www.calculationtime.com/calculators/variance-calculator

This report shows the calculation inputs, formula, assumptions and result for review. It is not legal, payroll, tax, engineering, financial or academic advice unless a qualified professional confirms the applicable rules.