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Unit–28: Measures of Dispersion: Standard Deviation

in this formula notes
x = Variable value or value of elements in a series
A = assumed mean
N = total number of elements
if we represent (x – A) by d’, then the formula becomes

S′  d 2 S  d ' 2
σ =   N   N

the above formulae (i) and (ii) are used for simple series. these formulae are slightly changed in the
case of calculation of standard deviation (s.D.) for discrete series and continuous series.

Formula for Discrete Series–

(i) By direct method

S fd 2
σ = N

in the above formula
σ = Standard Deviation
f = frequency of elements
d = (x – M) where M is arithmetic mean
N = total sum of frequencies

(iii) By short–cut method

S F d 2  S F d  ′ 2
′
σ = −  
N  N 
in the above formula
σ = Standard Deviation
f’ = frequency of elements
d = (x–A) where A is assumed mean
N = total sum of frequencies

Formula for Continuous Series–

(i) By direct method
S f d 2
σ = N
in the above formula
σ = Standard Deviation
f = frequency of elements

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