JEE Main 2024 · 31 January · Evening Shift · Mathematics · Statistics
C. 180180180
Mean, x=a+b+68+44+48+606=55x = \dfrac{a + b + 68 + 44 + 48 + 60}{6} = 55x=6a+b+68+44+48+60=55
⇒a+b+220=330⇒ a + b + 220 = 330⇒a+b+220=330
⇒a+b=110...(i)⇒ a + b = 110 . . . \left(i\right)⇒a+b=110...(i)
Variance, σ2=∑(xi−x)2n{\sigma}^{2} = \dfrac{\mathop{∑}_{}^{}{\left({x}_{i} - x\right)}^{2}}{n}σ2=n∑(xi−x)2
⇒σ2=(a−55)2+(b−55)2+132+112+72+526=194⇒ {\sigma}^{2} = \dfrac{{\left(a - 55\right)}^{2} + {\left(b - 55\right)}^{2} + {13}^{2} + {11}^{2} + {7}^{2} + {5}^{2}}{6} = 194⇒σ2=6(a−55)2+(b−55)2+132+112+72+52=194
⇒(a−55)2+(b−55)2+364=1164⇒ {\left(a - 55\right)}^{2} + {\left(b - 55\right)}^{2} + 364 = 1164⇒(a−55)2+(b−55)2+364=1164
⇒(110−b−55)2+(b−55)2=800⇒ {\left(110 - b - 55\right)}^{2} + {\left(b - 55\right)}^{2} = 800⇒(110−b−55)2+(b−55)2=800
⇒2(55−b)2=800⇒ 2{\left(55 - b\right)}^{2} = 800⇒2(55−b)2=800
⇒(55−b)=20⇒ \left(55 - b\right) = 20⇒(55−b)=20
⇒b=35⇒ b = 35⇒b=35
⇒a=75⇒ a = 75⇒a=75
⇒a+3b=75+105=180⇒ a + 3b = 75 + 105 = 180⇒a+3b=75+105=180
