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Math & Statistics

Standard Deviation Calculator

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Math & Statistics

Standard Deviation Calculator

Live answer4.062 sample SDmean 9 · population SD 3.6332 · squared-difference total 66 across 5 values
Live result4.062 sample SDmean 9 · population SD 3.6332 · squared-difference total 66 across 5 values
Formula used

Mean = sum of values ÷ n. Population standard deviation σ = √(Σ(x − mean)² ÷ n). Sample standard deviation s = √(Σ(x − mean)² ÷ (n − 1)).

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

Live math canvas

Your numbers, formula and explanation together

Standard Deviation Calculator: 4.062 sample SD. mean 9 · population SD 3.6332 · 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 standard deviation σ = √(Σ(x − mean)² ÷ n). Sample standard deviation s = √(Σ(x − mean)² ÷ (n − 1)).
  1. Apply the formulaMean = sum of values ÷ n. Population standard deviation σ = √(Σ(x − mean)² ÷ n). Sample standard deviation s = √(Σ(x − mean)² ÷ (n − 1)).4.062 sample SDmean 9 · population SD 3.6332 · 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 values in the data set. 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

4.062 sample SD

mean 9 · population SD 3.6332 · squared-difference total 66 across 5 values

Answer
4.062 sample SD
Live support
mean 9 · population SD 3.6332 · squared-difference total 66 across 5 values

Assumptions used

What this answer assumes

Use population standard deviation for the whole group; use sample standard deviation 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.
  • The population result divides by n. Use it when the entered values are the whole group being described.
  • The sample result divides by n − 1. Use it when the entered values are a sample used to estimate a wider population.
  • This calculator uses unweighted numeric values. Frequency tables, grouped classes and weighted standard deviation need a separate method.

Master’s Tip

How to use the result well

Master’s Tip: print the mean, squared-difference total and whether you used population or sample mode. Most standard-deviation mistakes come from using the wrong denominator or silently changing which values were included.

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

Denominator check

Sample vs population

Both results start from the same mean and squared-difference total. The denominator changes the interpretation.

ModeDenominatorStandard deviation
Population53.6332
Sample44.0620

Visual proof

Distance from mean

4791015Mean 9.0000 · squared total 66.0000Taller bars have stronger pull on the spread.

The bars show the squared distances from the mean before division and square root. That is the core audit trail for the statistic.

Visual grid

This number is one point on a larger pattern

Standard Deviation 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
4.062 sample SD

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

CalculationTime

Standard Deviation Calculation Report

Report date:

4.062 sample SDmean 9 · population SD 3.6332 · 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 standard deviation σ = √(Σ(x − mean)² ÷ n). Sample standard deviation s = √(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, so population standard deviation is √13.2 ≈ 3.6332. Sample variance is 66 ÷ 4 = 16.5, so sample standard deviation is √16.5 ≈ 4.0620.

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.
  • The population result divides by n. Use it when the entered values are the whole group being described.
  • The sample result divides by n − 1. Use it 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/standard-deviation-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.