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Maths · Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data

Assertion If i.e. =\mathbf{0 . 2 5}, \boldsymbol{\sigma}_{\boldsymbol{x}}=\mathb

Assertion If \( \boldsymbol{r}_{\boldsymbol{x} \boldsymbol{y}} \) i.e. \( \boldsymbol{r}(\boldsymbol{x}, \boldsymbol{y})=\mathbf{0 . 2 5}, \boldsymbol{\sigma}_{\boldsymbol{x}}=\mathbf{0 . 1}, \boldsymbol{\sigma}_{\boldsymbol{y}}= \) \( 4, \) then \( b_{y x}=10 \) Reason \( \boldsymbol{b}_{\boldsymbol{y} \boldsymbol{x}}=\boldsymbol{r} \frac{\boldsymbol{\sigma}_{\boldsymbol{y}}}{\boldsymbol{\sigma}_{\boldsymbol{x}}} \)

  • A. Both Assertion \&. Reason are individually true \& Reason is correct explanation of Assertion,
  • B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion
  • C. Assertion is true Reason is false.
  • D. Assertion is false Reason is true.

Step-by-step solution

Given r = 0.25, σ_x = 0.1, σ_y = 4. Using the formula b_yx = r * (σ_y/σ_x) = 0.25 * (4/0.1) = 0.25 * 40 = 10, so the assertion is true. The reason correctly states the formula for the regression coefficient and is the correct explanation.
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