Standard Deviation

Definition of " Standard Deviation

Formula of standard deviation

How to find standard deviation in Excel ?

Standard Deviation: It is Average Deviation of process output from their average

    

Standard deviation is denoted by σ, s, sigma

Standard deviation formula

** formula to find standard deviation in google doc and MS Excel ( if process 
output data are in cell B4 to b13 of excell sheet)

                                    =stdev(B4:B13)       

Example: we have below process output, find standard deviation

0.12, 0.14, 0.16, 0.18, 0.20

Solution

             

                    

Xi	Xi - x̄	( Xi - x̄)2
0.12	-0.04	0.0016
0.14	-0.02	0.0004
0.16	0.00	0
0.18	0.02	0.0004
0.20	0.04	0.0016
X̄ = 0.16		=  0.004

    

                     = 0.004

             

              

 

Let us understand standard deviation formula by easy method , 
by studying this you can easily memorize standard deviation formula

If we have some process output Xi  Where i = 1 to n

(ie, X1, X2, X3..........Xn)

Average of process output is  x̄

Now deviation of process output from their average is = Xi - x̄

(ie, X1 - x̄, X2 - x̄, X3 - x̄,.........Xn - x̄)

Now we do square of this ( Xi - x̄)2  (to eliminate -Ve value of deviation)

[ie, (XI - x̄)2, (X2 - x̄)2, (X3 - x̄)2,.........(Xn - x̄)2]

Now we do sum of this    

[ie, (X1 - x̄)2 + (X2 - x̄)2 + (X3 - x̄)2 + ......... + (Xn - x̄)2]

  

[ie, {(X1 - x̄)2 + (X2 - x̄)2 + (X3 - x̄)2 + ......... + (Xn - x̄)2}/n] =

(But for getting standard deviation we use n-1 instead n 
because one deviation value is zero which is not deviation)

[ie, {(X1 - x̄)2 + (X2 - x̄)2 + (X3 - x̄)2 + ......... + (Xn - x̄)2}/n - 1]

Now we do square root of above because we already made square