2√(17/21), or about 1.8.
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The standard deviation of 2 3 5 6 = 1.8257
For 1 2 2 3 4 5 5 5 5 6: σ=1.6865
For 3 5 8 7 2 4 6: σ=2.1602
For 2 4 5 6 8: σ=2.2361
Consider thatxd= x- Arithmetic meand211-1.5 = -0.50.2522-1.5 = 0.50.25=0.5Arithmetic mean = (1+2)/2 =1.5Standard deviation=ie .5= 0.70now Considerxd= x- Arithmetic meand211-2=-1122-2=0033-2=11Arithmetic mean= (1+2+3)/3 = 2 =2Standard deviation= = (2/2) = 1So the Standard deviation can increasenow Considerxd= x- Arithmetic meand211-1.25=-0.250.062522-1.25=0.750.562511-1.25=-0.250.062511-1.25=-0.250.0625Arithmetic mean= (1+2+1+1)/4= 1.25 = .75Standard deviation= = (0.75/4) = 0.4330So the Standard deviation can decreaseStandard deviation can either decrese or increase or remains the same