Question

The mean and variance of 5 observations
are 3 and 2 respectively. If three of the five
observations are 1, 3 and 5, find the values
of other two observations.​

Answer 1

The values  of other two observations is 2 and 4

Step-by-step explanation:

Let the third and fourth number be x an y respectively

Observations : 1,3,5,x,y

The mean and variance of 5 observations  are 3 and 2 respectively.

Mean of 5 observations = $\frac{1+3+5+x+y}{5}$

$3=\frac{1+3+5+x+y}{5}$

$15=9+x+y$

$6=x+y$---A

variance = $\frac{\sum(x_i-\bar{x})^2}{n}$

$2=\frac{(1-3)^2+(3-3)^2+(5-3)^2+(x-3)^2+(y-3)^2}{5}$

$10=(1-3)^2+(3-3)^2+(5-3)^2+(x-3)^2+(y-3)^2$

$10=8+(x-3)^2+(y-3)^2$

$2=x^2+9-6x+y^2+9-6y$

$2=x^2-6x+y^2-6y+18$

$2=x^2-6x+y^2-6y+18$

Substitute teh value of x from A

$2=(6-y)^2-6(6-y)+y^2-6y+18$

$y=2,4$

Substitute the value in A

$6=x+y$

At y = 2

$6=x+2$

x=4

At y =4

$6=x+4$

x=2

So, the values  of other two observations is 2 and 4

#Learn More:

The mean of five observation is 4.4 and there variance is 8.24 if 3 of the observation are 1,2 and 6 find the other observation

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