Identify the correct formula for calculating r using the step deviation method, where U and V are the step deviations of X and Y. Options: A . &nbsp r = N ∑ ( U i V i ) – N ( ∑ U i ) ( ∑ V i ) √ N ∑ U 2 i – ( ∑ U i ) 2 √ N ∑ V 2 i – ( ∑ V i ) 2 B . &nbsp r = N ∑ ( U i V i ) – ( ∑ U i ) ( ∑ V i ) √ N ∑ U 2 i – ( ∑ U i ) 2 √ N ∑ V 2 i – ( ∑ V i ) 2 C . &nbsp r = N ∑ ( U i V i ) – ( ∑ U i ) ( ∑ V i ) ( N ∑ U 2 i – ( ∑ U i ) 2 ) ( N ∑ V 2 i – ( ∑ V i ) 2 ) D . &nbsp r = N ∑ ( U i V i ) – N ( ∑ U i ) ( ∑ V i ) ( N ∑ U 2 i – ( ∑ U i ) 2 ) ( N ∑ V 2 i – ( ∑ V i ) 2 )

Answer: Option B : B The shortcut formula for calculating r is r = N ∑ ( U i V i ) – ( ∑ U i ) ( ∑ V i ) √ N ∑ U 2 i – ( ∑ U i ) 2 √ N ∑ V 2 i – ( ∑ V i ) 2

Identify the correct formula for calculating r using the step deviation m

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.

Options:

A .

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}}}

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}}}

C .

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})}

D .

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})}

Answer: Option B
:
B

The shortcut formula for calculating r is
$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$