Which one of the following is the absolute measure of dispersion for open ended distributions?
Options
ARange
BStandard deviation
CMean deviation
DQuartile deviation
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Measures of Central Tendency and DispersionPYQ May 25Question 4074 of 473
All Questions Correct Answer
✅ Option d — Quartile deviation
All Options:
- ARange
- BStandard deviation
- CMean deviation
- DQuartile deviation
Detailed Solution & Explanation
An open-ended distribution is one where the lower limit of the first class interval and/or the upper limit of the last class interval are not specified.
Let us evaluate the suitability of each measure of dispersion for open-ended distributions:
1. **Range**: Requires the absolute minimum and maximum values of the entire distribution, which are unknown in open-ended classes.
2. **Mean Deviation** and **Standard Deviation**: Require calculation of the class midpoints (mid-values) for all classes. Since the boundary values of open-ended classes are missing, midpoints cannot be computed.
3. **Quartile Deviation**: Depends only on the quartiles and , which are partition values calculated from the cumulative frequencies. Because and fall within the middle 50% of the distribution, their calculations are completely unaffected by open-ended extremities at either end.
Thus, Quartile Deviation is the only absolute measure of dispersion suitable for open-ended distributions.
Hence, **Option D** is the correct answer.
Let us evaluate the suitability of each measure of dispersion for open-ended distributions:
1. **Range**: Requires the absolute minimum and maximum values of the entire distribution, which are unknown in open-ended classes.
2. **Mean Deviation** and **Standard Deviation**: Require calculation of the class midpoints (mid-values) for all classes. Since the boundary values of open-ended classes are missing, midpoints cannot be computed.
3. **Quartile Deviation**: Depends only on the quartiles and , which are partition values calculated from the cumulative frequencies. Because and fall within the middle 50% of the distribution, their calculations are completely unaffected by open-ended extremities at either end.
Thus, Quartile Deviation is the only absolute measure of dispersion suitable for open-ended distributions.
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 SyllabusExam 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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