S2 = [ ∑ (xi – `X )2] / ( n – 1 )

∑ (Xi –`X )2 = ∑ ( X2 – 2 Xi`X + (`X )2 )

2`X constant (in sample) Then ∑ 2 Xi`X = 2`X ∑Xi

∑ (X–`X )2 = ∑ (Xi2 )– 2`X ∑(Xi) + ∑(`X )2

`X = ∑(Xi) / n Then ∑(Xi) = n`X , ∑(`X )2 = n(`X )2

= ∑ (Xi2 )– 2n(`X )2 + n(`X )2

= ∑ (Xi2 ) – n(`X )2 ,`X = ∑(Xi) / n

= ∑ (Xi2 ) – (∑Xi)2 / n

S2 = [∑ (Xi2 ) – (∑Xi )2 / n] / ( n – 1 ) ... (1)

Or

S2 = [( ∑Xi2 ) – n`X2 ] / ( n – 1 ) ... (2)