Correlation and RegressionMCQMTP Dec 22 - Series IQuestion 3697 of 188
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For n\displaystyle n pairs of observations, the coefficient of concurrent deviation is calculated as 1/3\displaystyle 1/\sqrt{3}. If there are 6\displaystyle 6 concurrent deviations, n=\displaystyle n=

Options

A11\displaystyle 11
B10\displaystyle 10
C9\displaystyle 9
D8\displaystyle 8
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Correct Answer

✅ Option b — 10\displaystyle 10

All Options:

  • A11\displaystyle 11
  • B10\displaystyle 10
  • C9\displaystyle 9
  • D8\displaystyle 8

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Detailed Solution & Explanation

The coefficient of concurrent deviation (rc\displaystyle r_c) is given by: rc=±±2c−mmr_c = \pm \sqrt{\pm \frac{2c - m}{m}} Given: - rc=13\displaystyle r_c = \frac{1}{\sqrt{3}} (which is positive) - c=6\displaystyle c = 6 is the number of concurrent deviations Since rc>0\displaystyle r_c > 0, we have 2c−m>0\displaystyle 2c - m > 0 and the formula becomes: rc=2c−mmr_c = \sqrt{\frac{2c - m}{m}} Squaring both sides: rc2=2c−mmr_c^2 = \frac{2c - m}{m} (13)2=2(6)−mm\left(\frac{1}{\sqrt{3}}\right)^2 = \frac{2(6) - m}{m} 13=12−mm\frac{1}{3} = \frac{12 - m}{m} Now, solve for m\displaystyle m by cross-multiplying: m=3(12−m)m = 3(12 - m) m=36−3mm = 36 - 3m m+3m=36m + 3m = 36 4m=36⇒m=94m = 36 \Rightarrow m = 9 Since m\displaystyle m is the number of deviations, we relate it to the number of pairs n\displaystyle n by: m=n−1m = n - 1 9=n−1⇒n=109 = n - 1 \Rightarrow n = 10 Therefore, the total number of pairs of observations is 10\displaystyle 10. 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.

Related Comparison Tables

Correlation vs Regression: Statistics for CA Foundation

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