Question

A.M. of two no.s is 10 and S.D. is 2; find nos.​

Answer 1

Answer:

14 and 16

Step-by-step explanation:

Let 2 nos. in A.P be "a" and "a+d"

A. T. Q

a+a+d=10

2a+d=10

d=2

a=14

So, 1st no. is 14

2nd is 16

Answer 2

Answer:

The values of a and b are $a=12,b=8$

Step-by-step explanation:

Let the two numbers be a and b.

Given that,the arithmetic mean of two numbers is 10.Hence we write

$\vec x=10=\frac{a+b}{2}= > a+b=20-- > (1)$

Also given that,

The standard deviation of the numbers is 2.Therefore,

$= > \sqrt{\frac{\Sigma x_{i}^2}{n}-\bar x^2}=2$

Here n=2 therefore,

$\frac{a^{2}+b^{2}}{2} -10^{2}=4\\= > a^{2}+b^{2}=208-- > (2)$

Squaring equation 1,we get

$a^{2}+b^{2}+2ab=400-- > (3)$

Substituting equation 2 in equation 3,we get

$208+2ab=400= > 2ab=192= > ab=96$

$(a-b)^{2}=a^{2}+b^{2}-2ab=208-192=16\\= > a-b=4-- > (4)$

Solving equation 1 and equation 4,we get $a=12,b=8$

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