The possible value of x if SD of the numbers 2, 3, 2x and 11 is 3.5 is equal to

Step-by-step solution

Given Standard deviation of 2, 3, 2x and 11 is 3.5. aligned & Mean ( x )= 2+3+2 x+11 4 = 8+x 2 & Now, _ i=1 ^4 (x_i- x )^2 2- ( 8+x 2 ) ^2+ 3- ( 8+x 2 ) ^2 &+ 2 x- ( 8+x 2 ) ^2+ 11- ( 8+x 2 ) ^2 &= ( 4+x 2 )^2+ ( 2+x 2 )^2+ ( 3 x-8 2 )^2+ ( 14-x 2 )^2 aligned aligned & SD = [ array l [ 4+x 4 )^2+ ( 2+x 2 )^2+ ( 3 x-8 2 )^2 + ( 14-x 2 )^2 array ] & (3 5)^2 4= 1 4 aligned aligned & [16+x^2+8 x+4+x^2+4 x+9 x^2+64-48 x . & . +196+x^2-28 x ] & & 12 x^2-64 x+84=0 & x=3,7 / 3 aligned