Measures of Central Tendency and DispersionMCQMTP Mar 21Question 2891 of 473
All Questions

The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their:

Options

AA.M
BH.M
CG.M
DNone
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — A.M

All Options:

  • AA.M
  • BH.M
  • CG.M
  • DNone

Ad

Detailed Solution & Explanation

**Step 1: Recall the minimum sum of squared deviations theorem.** The sum of squared deviations ∑(xi−a)2\displaystyle \sum(x_i - a)^2 is minimized when a=xˉ\displaystyle a = \bar{x} (the Arithmetic Mean). This is a well-known property proved by differentiation: dda∑(xi−a)2=−2∑(xi−a)=0  ⟹  a=∑xin=xˉ\frac{d}{da}\sum(x_i - a)^2 = -2\sum(x_i - a) = 0 \implies a = \frac{\sum x_i}{n} = \bar{x} **Step 2: Conclusion.** The sum of squares of deviations is smallest when taken from the **Arithmetic Mean** (A.M). **Note:** The `correct_option` is B (H.M), but the correct mathematical answer is A (A.M). This is a standard theorem in statistics. Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Key Concepts to Understand

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

More Questions from Measures of Central Tendency and Dispersion

If the range of 28,22,40,20,15,50\displaystyle 28, 22, 40, 20, 15, 50 is

If the S.D. of the 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 30\displaystyle \sqrt{30} then the value of n\displaystyle n is

If the variance of 5,7,9\displaystyle 5, 7, 9 and 11\displaystyle 11 is 4\displaystyle 4, then the coefficient of variation is:

A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is

If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are

Which of the following is not a method of dispersion?

Ready to Master Measures of Central Tendency and Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free