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Given below are the diameters of circles...

Given below are the diameters of circles (in mm) drawn in a design.
`{:("Diameter",33-36,37-40,41-44,45-48,49-52),("Number of Circles",15,17,21,22,25):}`
Calculate the mean diameter of the circles, variance and standard deviation.

Text Solution

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`{(C.I,fi,x_i,yi,fiyi,fiyi^2),(32.5-36.6,15,34.5,-2,-30,60),(32.5-40.5,17,38.5,-1,-17,17),(40.5-44.5,21,42.5,0,0,0),(44.5-48.5,22,46.5,1,22,22),(48.5-52.5,25,50.5,2,50,100),(0,0,0,0,sumf_i=100,(sumf_iy_i^2=199)):}`
`y_i=(x_i-42.5)/4`
` :. A= 42.5 , h =4 , N=100 , sumf_iy_i =25 and sum f_iy_i^2 =199`
`mean =( 42.5 + (25)/(100) xx4) = 43.5`
`sigma^2=(sum(fiu_i^2)/N-(sum(fiu_i)/N)^2)`
`(199/100-(25/100)^4)xx4`
`sigma^2=30.84`
SD`=sigma=sqrt(30.84)=5.553`
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