Measures of Central Tendency and DispersionMCQMTP Apr 21Question 3174 of 473
All Questions

Which measure of dispersion is based on all the observations?

Options

AMean Deviation
BStandard Deviation
CQuartile Deviation
DA and B but not C
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Correct Answer

✅ Option d — A and B but not C

All Options:

  • AMean Deviation
  • BStandard Deviation
  • CQuartile Deviation
  • DA and B but not C

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Detailed Solution & Explanation

**Analysis of each measure:** - **Range:** Based only on 2 observations (max and min). - **Quartile Deviation (QD):** Based only on the middle 50% of observations (Q1\displaystyle Q_1 and Q3\displaystyle Q_3); extreme values are ignored. - **Mean Deviation (MD):** Calculated using all observations — MD=∑∣xi−xˉ∣n\displaystyle MD = \frac{\sum|x_i - \bar{x}|}{n}; uses all n\displaystyle n values. - **Standard Deviation (SD):** Calculated using all observations — σ=∑(xi−xˉ)2n\displaystyle \sigma = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n}}; uses all n\displaystyle n values. Both MD and SD use all observations. The best answer among the given options is **Option D: A and B but not C** (Mean Deviation AND Standard Deviation, but NOT Quartile Deviation). The given `correct_option` 'a' (Mean Deviation only) is incomplete since SD also uses all observations. 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.

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