Measures of Central Tendency and DispersionMCQMTP Nov 20Question 3103 of 473
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The mean deviation about Mode for the numbers 4/11,6/11,8/11,9/11,12/11,8/11\displaystyle 4/11, 6/11, 8/11, 9/11, 12/11, 8/11 is

Options

A9/15\displaystyle 9/15
B12\displaystyle 12
C6/11\displaystyle 6/11
D1/6\displaystyle 1/6
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Correct Answer

✅ Option d — 1/6\displaystyle 1/6

All Options:

  • A9/15\displaystyle 9/15
  • B12\displaystyle 12
  • C6/11\displaystyle 6/11
  • D1/6\displaystyle 1/6

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Detailed Solution & Explanation

We are given the observations: 4/11,6/11,8/11,9/11,12/11,8/11\displaystyle 4/11, 6/11, 8/11, 9/11, 12/11, 8/11. The number of observations is n=6\displaystyle n = 6. 1. Find the Mode: The mode is the observation with the highest frequency. Here, 8/11\displaystyle 8/11 appears twice while all other observations appear once. Thus, Mode=8/11\displaystyle \text{Mode} = 8/11. 2. Find absolute deviations from the mode ∣xi−Mode∣\displaystyle |x_i - \text{Mode}|: - ∣4/11−8/11∣=4/11\displaystyle |4/11 - 8/11| = 4/11 - ∣6/11−8/11∣=2/11\displaystyle |6/11 - 8/11| = 2/11 - ∣8/11−8/11∣=0\displaystyle |8/11 - 8/11| = 0 - ∣9/11−8/11∣=1/11\displaystyle |9/11 - 8/11| = 1/11 - ∣12/11−8/11∣=4/11\displaystyle |12/11 - 8/11| = 4/11 - ∣8/11−8/11∣=0\displaystyle |8/11 - 8/11| = 0 3. Calculate sum of absolute deviations: ∑∣xi−Mode∣=4+2+0+1+4+011=1111=1\sum |x_i - \text{Mode}| = \frac{4 + 2 + 0 + 1 + 4 + 0}{11} = \frac{11}{11} = 1 4. Calculate Mean Deviation about Mode: M.D.=16\text{M.D.} = \frac{1}{6} Hence, **Option D** 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

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

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

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