Measures of Central Tendency and DispersionPYQ Sept 25Question 4178 of 473
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A data set has first eleven positive multiples of 6. The semi inter-quartile range is

Options

A12
B24
C18
D36
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Correct Answer

✅ Option c — 18

All Options:

  • A12
  • B24
  • C18
  • D36

Detailed Solution & Explanation

Let us find the semi inter-quartile range (also known as the Quartile Deviation) of the first eleven positive multiples of 6\displaystyle 6.
1. **Write down the dataset** in ascending order:
6,12,18,24,30,36,42,48,54,60,666, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66
Here, the number of observations is n=11\displaystyle n = 11.
2. **Calculate the First Quartile (Q1\displaystyle Q_1)**:
Q1=Value of (n+14)-th term=Value of (11+14)-th term=3rd termQ_1 = \text{Value of } \left(\frac{n+1}{4}\right)\text{-th term} = \text{Value of } \left(\frac{11+1}{4}\right)\text{-th term} = \text{3rd term}
The 3rd term in our dataset is 18\displaystyle 18. Therefore, Q1=18\displaystyle Q_1 = 18.
3. **Calculate the Third Quartile (Q3\displaystyle Q_3)**:
Q3=Value of 3(n+14)-th term=Value of 3(3)-th term=9th termQ_3 = \text{Value of } 3\left(\frac{n+1}{4}\right)\text{-th term} = \text{Value of } 3(3)\text{-th term} = \text{9th term}
The 9th term in our dataset is 54\displaystyle 54. Therefore, Q3=54\displaystyle Q_3 = 54.
4. **Calculate the Semi Inter-Quartile Range (QD\displaystyle QD)**:
QD=Q3−Q12QD = \frac{Q_3 - Q_1}{2}
QD=54−182=362=18QD = \frac{54 - 18}{2} = \frac{36}{2} = 18
Therefore, the semi inter-quartile range is 18\displaystyle 18.
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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