Identify the correct formula for calculating r using the step deviation method- where U and V are the step deviations of X and Y-A- r - N - U i V i - N - U i - V i - N - U i 2- U i 2- N - V i 2- V i 2B- r - N - U i V i - U i - V i - N - U i 2- U i 2- N - V i 2- V i 2N - U i V i - U i - V i C- r -N U i - V i - N - V i 2- V i - V i 2D- r - N - i U i V i - N - U i i - V i - N - U i 2- U i 2 N - V i 2- V i 2

The correct option is B r=N ∑ (U_i V_i) – (∑ U_i) (∑ V_i)/√(N ∑ U_i^2 –(∑ U_i)^2)√(N ∑ V_i^2 –(∑ V_i)^2) The shortcut formula for calculating r is r=N ∑ (U_i ...

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Byju's Answer

Standard XI

Statistics

Step Deviation Method to Calculate R

Identify the ...

Question

Identify the correct formula for calculating r using the step deviation method, where U and V are the step deviations of X and Y.

$r = \frac{N \sum (U_{i} V_{i}) - N (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$

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$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$

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$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{(N \sum U_{i}^{2} - (\sum U_{i})^{2}) (N \sum V_{i}^{2} - (\sum V_{i})^{2})}$

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$r = \frac{N \sum (U_{i} V_{i}) - N (\sum U_{i}) (\sum V_{i})}{(N \sum U_{i}^{2} - (\sum U_{i})^{2}) (N \sum V_{i}^{2} - (\sum V_{i})^{2})}$

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Solution

The correct option is B
$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$

The shortcut formula for calculating r is

$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$

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Similar questions

An asteroid of mass M is approaching earth, initially at a distance of $10 R_{e}$ with speed $V_{i}$ . It hits the earth with a speed $V_{f}$ (Consider $R_{e}$ and $M_{e}$ as radius and mass of the earth), then:

Function Domain Range

(i)sinx (P) R (L) [-1, 1]

(ii) cosx (Q) R - {n $π$ } (M) R

(iii) tanx (R) R- {(2n + 1}) $\frac{π}{2}$ } (N) $(- \infty$ , -1] u [1, $\infty$ )

(iv) cosecx

(v) secx

(vi) cotx

How many of the following are matched correct?

(i) -P-L, (ii) -P-L, (iii)-R-M, (iv) -Q-N, (v) -R-N, (vi) -Q-M

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Q. If

x_{1}, x_{2}, x_{3}, \dots, x_{n}

are n-values of a variable x such that

\sum_{i = 1}^{n} u_{i} = 90

and

\sum_{i = 1}^{n} V_{i} = 150

where

u_{i} = 2 x_{i} - 3

and

V_{i} = 3 x_{i} - 4

, for i = 1, 2, 3, 4, …, n, then the value of n will be

$\begin{matrix} Function & Domain & Range (i) sinx & (P) R & (L) [-1, 1] (ii) cos x & (Q) R-n π & (M) R (iii) tan x & (R) R- {(2n+1)} & (N) (- \infty, -1] \cup [1, \infty) (iv) cosec x (v) sec x (vi) cot x \end{matrix}$