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13.Statistics
hard
ધારોકે $8$ સંખ્યાઓ $x, y, 10,12,6,12,4,8$ ના મધ્યક અને વિયરણ અનુક્રમે $9$ અને $9.25$ છે. જો $x > y$ હોય, તો $3 x-2 y=.........$.
A
$24$
B
$25$
C
$23$
D
$22$
(JEE MAIN-2023)
Solution
$\frac{x+y+52}{8}=9 \Rightarrow x+y=20$
For variance
$x-9, y-9,3,3,1,-5,-1,-3$
$\bar{x}=0$
$\therefore \frac{(x-9)^2+(y-9)^2+54}{8}-0^2=9.25$
$(x-9)^2+(11-x)^2=20$
$x=7 \text { or } 13 \therefore y=13,7$
$3 x-2 y=3 \times 13-2 \times 7=25$
Standard 11
Mathematics
