Let the mean and the variance of 6 observation a ,b ,68 ,44 ,48 ,60 be 55 and 194 , respectively if ab, then a+3b is

Question

Let the mean and the variance of 6 observation a ,b ,68 ,44 ,48 ,60 be 55 and 194 , respectively if a>b, then a+3b is

Accepted Answer

Correct answer: C. (c) a ,b ,68 ,44 ,48 ,60 Mean=55 Variance=194 a>b a+b+68+44+48+606=55 ⇒220+a+b=330 ∴a+b=110 … … (i ) Also, (x_i-x)^2n=194 ⇒ (a-55 )^2+ (b-55 )^2+ (68-55 )^2+ (44-55 )^2 + (48-55 )^2+ (60-55 )^2=194 6 ⇒ (a-55 )^2+ (b-55 )^2+169+121+49+25=1164 ⇒ (a-55 )^2+ (b-55 )^2=1164-364=800a^2+3025-110a+b^2+3025-110b=800 ⇒a^2+b^2=800-6050+12100a^2+b^2=6850 … … . ( ii ) Solve (1) ∖ \& (2); a=75 ,b=35 ∴a+3b=75+3 (35 )=75+105=180

$Let the mean and the variance of 6 observation a, b, 68, 44, 48, 60 be 55 and 194 , respectively if a > b, then a + 3 b is$

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