Measures of Central Tendency and DispersionMCQPYQ June 23Question 3226 of 473
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For a given set of normally distributed data, the following statistical parameters are known: Mean =6\displaystyle = 6, Standard deviation =2.6\displaystyle = 2.6, Median =5\displaystyle = 5 and Quartile deviation =1.5\displaystyle = 1.5, then the coefficient of quartile deviation equals to

Options

A30\displaystyle 30
B32\displaystyle 32
C25\displaystyle 25
D39\displaystyle 39
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Correct Answer

✅ Option a — 30\displaystyle 30

All Options:

  • A30\displaystyle 30
  • B32\displaystyle 32
  • C25\displaystyle 25
  • D39\displaystyle 39

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Detailed Solution & Explanation

We are given the parameters for a normal distribution: - Median = 5\displaystyle 5 - Quartile Deviation (Q.D.) = 1.5\displaystyle 1.5 The coefficient of quartile deviation is defined as: Coefficient of Q.D.=Q.D.Median×100\text{Coefficient of Q.D.} = \frac{\text{Q.D.}}{\text{Median}} \times 100 Coefficient of Q.D.=1.55×100=30%\text{Coefficient of Q.D.} = \frac{1.5}{5} \times 100 = 30\% 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.

Median

The middle value of a data set when arranged in ascending or descending order. It divides the distribution into two equal halves. For even n: Median = average of (n/2)th and (n/2 + 1)th values. It is NOT affected by extreme values.

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

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

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