Chapter 15

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Example 3 Show that the two formulae for the standard deviation of ungrouped data. ( )2 x xi n − σ = and 2 xi x2 n σ′ = − are equivalent. Solution We have ( )2 x xi − = ( 2 )2 2 x x x xi i− + = 2 2 2 x x x xi + − +i = 2 ( )2 x x x xi − +2 i 1 = 2 2 ( ) 2 x x nx n xi − + = 2 2 x nxi −

  Standards, Data, Formulae, Deviation, Standard deviation