If the coefficient of correlation between x and y is 0.5 , the covariance is 16 and the Standard Deviation of y is

Option b: 8. Solution: Finding standard deviation of y: Given: - r = 0.5 - (x,y) = 16 - = 4 (from variance of x = 16 , i.e., = 4 ) Formula: r = (x,y) × 0.5 = 16/4 × 0.5 × 4 × = 16 2 = 16 = 8 Hence, Option B is the correct answer.

If the coefficient of correlation between x and y is $0.5$, the covariance is $16$ and the Standard Deviation of y is

The correct answer is Option b: $8$. **Finding standard deviation of y:** Given: - $r = 0.5$ - $\\text{Cov}(x,y) = 16$ - $\\sigma_x = 4$ (from variance of $x = 16$, i.e., $\\sigma_x = 4$) **Formula:** $$r = \\frac{\\text{Cov}(x,y)}{\\sigma_x \\cdot \\sigma_y}$$ $$0.5 = \\frac{16}{4 \\times \\sigma_y}$$ $$0.5 \\times 4 \\times \\sigma_y = 16$$ $$2\\sigma_y = 16$$ $$\\sigma_y = 8$$ Hence, **Option B** is the correct answer.

Correlation and RegressionMCQMTP Dec 23 Series IQuestion 3664 of 188

All Questions

If the coefficient of correlation between x and y is $\displaystyle 0.5$ , the covariance is $\displaystyle 16$ and the Standard Deviation of y is

Options

\displaystyle 4

\displaystyle 8

\displaystyle 16

\displaystyle 64

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Correct Answer

✅ Option b — $\displaystyle 8$

All Options:

A $\displaystyle 4$
B $\displaystyle 8$
C $\displaystyle 16$
D $\displaystyle 64$

Detailed Solution & Explanation

**Finding standard deviation of y:** Given: -

\displaystyle r = 0.5

\displaystyle \\text{Cov}(x,y) = 16

\displaystyle \\sigma_x = 4

(from variance of

\displaystyle x = 16

, i.e.,

\displaystyle \\sigma_x = 4

) **Formula:**

r = \\frac{\\text{Cov}(x,y)}{\\sigma_x \\cdot \\sigma_y}

0.5 = \\frac{16}{4 \\times \\sigma_y}

0.5 \\times 4 \\times \\sigma_y = 16

2\\sigma_y = 16

\\sigma_y = 8

Hence, **Option B** is the correct answer.

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Correlation

A statistical measure that expresses the extent to which two variables are linearly related.

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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If the coefficient of correlation between x and y is 0.5\displaystyle 0.50.5, the covariance is 16\displaystyle 1616 and the Standard Deviation of y is