Q. 45.0( 2 Votes )

The standard devi

Answer :

Let the observations be x1, x2, x3….x20


Given SD =


Formula for SD =


Where N = 20, SD =


If each observation is multiplied by 2, we get new set of observations.


Let the new observations be y1, y2, y3….y20


New Standard Deviation SD’ =


We know that and


But yi = 2xi


Therefore,


Substituting in the SD’ formula,


SD’ =


=


= 2 × SD = 2


Formula relating SD and Variance is Variance = SD2


So Variance = (22 = 20


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