Measures of Central Tendency and DispersionPYQ Sept 25Question 4172 of 473
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Best measure of Dispersion for open-end classification is the _______, which does not change with the change of _________.

Options

AQuartile Deviation, Scale
BStandard Deviation, Scale
CQuartile Deviation, Origin
DStandard Deviation, Origin
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Correct Answer

✅ Option c — Quartile Deviation, Origin

All Options:

  • AQuartile Deviation, Scale
  • BStandard Deviation, Scale
  • CQuartile Deviation, Origin
  • DStandard Deviation, Origin

Detailed Solution & Explanation

Let us analyze the measures of dispersion for open-end classifications:
1. **Open-end Classification**: A frequency distribution where the lower limit of the first class interval and/or the upper limit of the last class interval are not specified. In such cases, standard deviation and range cannot be calculated because they require the mid-values or extreme values of all classes.
2. **Quartile Deviation**: The Quartile Deviation (QD\displaystyle QD) is calculated using the first quartile (Q1\displaystyle Q_1) and third quartile (Q3\displaystyle Q_3):
QD=Q3−Q12QD = \frac{Q_3 - Q_1}{2}
Since Q1\displaystyle Q_1 and Q3\displaystyle Q_3 only depend on the middle 50%\displaystyle 50\% of the observations, they are unaffected by the open-ended outer classes. Thus, Quartile Deviation is the best measure of dispersion for open-end classification.
3. **Effect of Origin**: All measures of dispersion (including Quartile Deviation) are independent of the change of origin. This means that if a constant is added or subtracted from each observation, the Quartile Deviation remains unchanged.
Therefore, the best measure of dispersion is the Quartile Deviation, which does not change with a change of origin.
Hence, **Option C** 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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