If the standard deviation of the numbers 2,3,2x and 11 is 3.5, then find the possible values of x.

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Please find below the solution to the asked query:

We have:2,3,2x and 11Meanm=2+3+2x+114=16+2x4=4+x24+x2-2=2+x24+x2-3=1+x24+x2-2x=4-3x24+x2-11=x2-7Standard Deviation=3.52+x22+1+x2+4-3x22+x2-724=3.5=3510=72Squarring both sides, we get:2+x22+1+x2+4-3x22+x2-724=4942+x22+1+x2+4-3x22+x2-72=494+x24+2+x24+8-3x24+x-1424=494+x2+2+x2+8-3x2+x-142=19616+x2+8x+4+x2+4x+64+9x2-48x+x2+196-28x=19612x2-64x+280-196=012x2-64x+84=03x2-16x+21=03x2-9x-7x+21=03xx-3-7x-3=0x-33x-7=0Hencex=3 or x=73

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