The mean of five observations is 5 and their | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the five observations be $1, 3, 8, x,$ and $y$.Given mean $\mu = 5$,so $\frac{1 + 3 + 8 + x + y}{5} = 5$.$12 + x + y = 25 \Rightarrow x + y =

Vedclass · Accepted Answer

$4 : 9$

Vedclass · Answer

(B) Let the five observations be $1, 3, 8, x,$ and $y$.Given mean $\mu = 5$,so $\frac{1 + 3 + 8 + x + y}{5} = 5$.$12 + x + y = 25 \Rightarrow x + y = 13$ (Equation $1$).Given variance $\sigma^2 = 9.20$,using the formula $\sigma^2 = \frac{\sum x_i^2}{N} - \mu^2$:$9.2 = \frac{1^2 + 3^2 + 8^2 + x^2 + y^2}{5} - 5^2$.$9.2 = \frac{1 + 9 + 64 + x^2 + y^2}{5} - 25$.$34.2 = \frac{74 + x^2 + y^2}{5} \Rightarrow 171 = 74 + x^2 + y^2$.$x^2 + y^2 = 97$ (Equation $2$).We know $(x + y)^2 = x^2 + y^2 + 2xy$,so $13^2 = 97 + 2xy$.$169 - 97 = 2xy$ $\Rightarrow 72 = 2xy$ $\Rightarrow xy = 36$.Solving $x + y = 13$ and $xy = 36$,the quadratic equation $t^2 - 13t + 36 = 0$ gives $(t - 4)(t - 9) = 0$.Thus,the two observations are $4$ and $9$.The ratio is $\frac{4}{9}$ or $\frac{9}{4}$.

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1, 3$ and $8$,then the ratio of the other two observations is

Similar Questions

The mean of $5$ numbers is $18$. If one number is excluded,their mean becomes $16$. Then the excluded number is

The mean and variance of $7$ observations are $8$ and $16$ respectively. If the first five observations are $2, 4, 10, 12, 14$,then the absolute difference of the remaining two observations is

The mean of $n$ items is $\bar x$. If the first term is increased by $1$,the second by $2$,and so on,then the new mean is:

The average marks of boys in a class is $40$ and that of girls is $45$. The average marks of both boys and girls combined is $42$. Then the percentage of boys in the class is (in $\%$)

The range of the observations $2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module