Consider three observations a, b and c such t | vedclass

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

Question

(D) Given observations are $a, b, c$ with $b = a + c$.The mean $\bar{x} = \frac{a + b + c}{3}$.Substituting $a + c = b$,we get $\bar{x} = \frac{b + b}

Vedclass · Accepted Answer

$b^{2} = 3(a^{2} + c^{2}) - 9d^{2}$

Vedclass · Answer

(D) Given observations are $a, b, c$ with $b = a + c$.The mean $\bar{x} = \frac{a + b + c}{3}$.Substituting $a + c = b$,we get $\bar{x} = \frac{b + b}{3} = \frac{2b}{3}$.The standard deviation of $a + 2, b + 2, c + 2$ is the same as the standard deviation of $a, b, c$,which is $d$.Thus,$d^{2} = \frac{a^{2} + b^{2} + c^{2}}{3} - (\bar{x})^{2}$.Substituting $\bar{x} = \frac{2b}{3}$,we have $d^{2} = \frac{a^{2} + b^{2} + c^{2}}{3} - \frac{4b^{2}}{9}$.Multiplying by $9$,we get $9d^{2} = 3(a^{2} + b^{2} + c^{2}) - 4b^{2}$.$9d^{2} = 3(a^{2} + c^{2}) + 3b^{2} - 4b^{2}$.$9d^{2} = 3(a^{2} + c^{2}) - b^{2}$.Therefore,$b^{2} = 3(a^{2} + c^{2}) - 9d^{2}$.

List-$I$	List-$II$
$(i) P$	$(A) (0, 0)$
$(ii) Q$	$(B) (6, 0)$
$(iii) R$	$(C) (-2, 1)$
$(iv) S$	$(D) (-6, 0)$
	$(E) (-6, -3)$
	$(F) (-6, 3)$

Consider three observations $a, b$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following is true?

Similar Questions

In a potentiometer experiment,the balancing length with a cell is $240\,cm$. On shunting the cell with a resistance of $2\,\Omega$,the balancing length becomes $120\,cm$. The internal resistance of the cell is ................... $\Omega$.

Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = 4$. Then $\int_{0}^{a} f(x)g(x) dx$ is equal to

If $2x + 3y = 5$ is the perpendicular bisector of the line segment joining the points $A\left(1, \frac{1}{3}\right)$ and $B$,then $B$ is equal to

Which of the following plants are used as green manure in crop fields and sandy soils?

Vedclass Test Series

Exam Paper Generator

Online Exam Module