If the mean and the standard deviation of the data 3,5,7, a , b are 5 and 2 respectively, then a and b are the roots of the equation :

Question

If the mean and the standard deviation of the data 3,5,7, a , b are 5 and 2 respectively, then a and b are the roots of the equation : (A) 2 x2-20 x+19=0 (B) x2-10 x+19=0 (C) x2-10 x+18=0 (D) x2-20 x+18=0

Tardigrade Admin · Accepted Answer

Mean =5 (3+5+7+a+b/5)=5 a+b=10 dots(i) S.d. =2 ⇒ √( displaystyle∑i=15(xi- barx)2/5)=2 (3-5)2+(5-5)2+(7-5)2+(a-5)2+(b-5)2=20 ⇒ 4+0+4+(a-5)2+(b-5)2=20 a2+b2-10(a+b)+50=12 (a+b)2-2 a b-100+50=12 a b=19 dots(ii) Equation is x2-10 x+19=0

Q. If the mean and the standard deviation of the data $3, 5, 7, a, b$ are $5$ and $2$ respectively, then a and $b$ are the roots of the equation :

$2 x^{2} - 20 x + 19 = 0$

$x^{2} - 10 x + 19 = 0$

$x^{2} - 10 x + 18 = 0$

$x^{2} - 20 x + 18 = 0$

Q. If the mean and the standard deviation of the data 3,5,7,a,b are 5 and 2 respectively, then a and b are the roots of the equation :

2x2−20x+19=0

x2−10x+19=0

x2−10x+18=0

x2−20x+18=0

Mean =5 53+5+7+a+b​=5 a+b=10…(i) S.d. =2⇒5i=1∑5​(xi​−xˉ)2​​=2 (3−5)2+(5−5)2+(7−5)2+(a−5)2+(b−5)2=20 ⇒4+0+4+(a−5)2+(b−5)2=20 a2+b2−10(a+b)+50=12 (a+b)2−2ab−100+50=12 ab=19…(ii) Equation is x2−10x+19=0

Q. If the mean and the standard deviation of the data $3, 5, 7, a, b$ are $5$ and $2$ respectively, then a and $b$ are the roots of the equation :

$2 x^{2} - 20 x + 19 = 0$

$x^{2} - 10 x + 19 = 0$

$x^{2} - 10 x + 18 = 0$

$x^{2} - 20 x + 18 = 0$