Measures of Central Tendency and DispersionMCQPYQ Sep 24 Series IQuestion 2941 of 473
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The AM of 15 observations is 9 and the AM of first 9 observations is 11 and then AM of remaining observations is

Options

A11
B6
C5
D9
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Correct Answer

✅ Option b — 6

All Options:

  • A11
  • B6
  • C5
  • D9

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Detailed Solution & Explanation

We are given: - Total number of observations: N=15\displaystyle N = 15 - Arithmetic mean of all 15 observations: xˉ=9\displaystyle \bar{x} = 9 - Sum of all 15 observations: Sum15=15×9=135\displaystyle \text{Sum}_{15} = 15 \times 9 = 135 - Number of observations in the first group: n1=9\displaystyle n_1 = 9 - Arithmetic mean of the first 9 observations: xˉ1=11\displaystyle \bar{x}_1 = 11 - Sum of the first 9 observations: Sum9=9×11=99\displaystyle \text{Sum}_9 = 9 \times 11 = 99 - Number of remaining observations: n2=15−9=6\displaystyle n_2 = 15 - 9 = 6 - Sum of the remaining 6 observations: Sum6=Sum15−Sum9=135−99=36\displaystyle \text{Sum}_6 = \text{Sum}_{15} - \text{Sum}_9 = 135 - 99 = 36 Calculating the arithmetic mean of the remaining observations: xˉ2=Sum6n2=366=6\bar{x}_2 = \frac{\text{Sum}_6}{n_2} = \frac{36}{6} = 6 Hence, **Option B** 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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