Standard Deviation Calculator

To calculate a Standard or Population Standard Deviation,
Upper/ Lower Control Levels (UCL/LCL) and
Process Capability (Cpk)

Standard Deviation
Standard Deviation
Population Standard Deviation
Population Standard Deviation
To solve the equations for S we need to find the values for:
X = Sample Value(s)
n = Number of Samples taken
n-1 = Number of Samples taken minus 1
M = Average of all Sample Values
For sum of x-m2 the Sum Symbol just means ‘The Sum Of’, so we subtract the Mean value (M) from each reading value (X) and then multiply each result by itself. Finally add all of the totals together.

Enter your Sample values below separated by commas


[n] Samples [n-1] Samples-1 [M] Average
5 4 3
Use this Table to find Sum of (X-M)^2
Readings [n] Value [X] Mean Avg [M] X-M [X-M]^2
1 13 -24
2 23 -11
3 33 00
4 43 11
5 53 24
Sum of (X-M)^210
Summary:
Sum of (X-M)^2 = 10
(n-1) = 4
(n) = 5
Now find Standard Deviation using the formula
Standard Deviation
S = √Sum of (X-M)^2 / √n-1
S = √10 / √4
S = 3.1623 / 2
S = 1.5811

Standard Deviation = 1.5811
Now Population Standard Deviation
Population Standard Deviation
S = √Sum of (X-M)^2 / √n
S = √10 / √5
S = 3.1623 / 2.2361
S = 1.4142

Population Standard Deviation = 1.4142
Determine Upper and Lower Control Limits UCL LCL
3 * StDev = 4.7434
Upper Control Limit (UCL) = Average + 3 * StDev
Lower Control Limit (LCL) = Average - 3 * StDev
UCL = 7.7434
LCL = -1.7434
Determine Process Capability Cpk
CpkU = UCL - Average / 3 * StDev
CpkL = Average - LCL / 3 * StDev
CpkU = 7.1109
CpkL = 3.3675
Use the lower value for Cpk Value. A Cpk of 1.33 is desired.
Cpk = 3.3675

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