If the variance of the numbers 2,3,11 and x is 49 4 , then the values of x are

Step-by-step solution

Mean of given number is 2+3+11+x 4 i.e. 16+x 4 aligned & Variance = 1 n ( x _ i - x )^2 & 49 4 = 1 4 [ ( 16+ x 4 -2 )^2+ ( 16+ x 4 -3 )^2+ ( 16+ x 4 -11 )^2+ ( 16+ x 4 - x )^2 ] & 49= (8+ x )^2 16 + (4+ x )^2 16 + ( x -28)^2 16 + (16-3 x )^2 16 & (49)(16)= (64+ x ^2+16 x )+ (16+ x ^2+8 x ) aligned aligned & + ( x ^2-56 x +784 )+ (256+9 x ^2-96 x ) & 784=12 x ^2-128 x +80+784+256 & 12 x ^2-128 x +336=0 & 3 x ^2-32 x +84=0 & x = 32 (32)^2-(4)(3)(84) 2(3) = 32 1024-1008 6 = 32 4 6 & x = 36 6 or x = 28 6 & x =6, 14 3 a