Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 2859 of 473
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If total frequencies of three series are 50, 60 and 90 and their means are 12, 15 and 20 respectively, then the mean of their composite series is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $16.5$

All Options:

  • A$16$
  • B$15.5$
  • C$16.5$
  • D$14.5$

Detailed Solution & Explanation

**Step 1: State the given data.**
SeriesFrequency (ni\displaystyle n_i)Mean (xˉi\displaystyle xˉi\displaystyle \bar{x}_i)Total (nixˉi\displaystyle n_i xˉi\displaystyle \bar{x}_i)
15012600
26015900
390201800
**Step 2: Compute combined mean using the formula.** xˉcombined=n1xˉ1+n2xˉ2+n3xˉ3n1+n2+n3\displaystyle \bar{x}_{combined} = \frac{n_1xˉ1+n2\displaystyle \bar{x}_1 + n_2xˉ2+n3\displaystyle \bar{x}_2 + n_3xˉ3\displaystyle \bar{x}_3}{n_1 + n_2 + n_3} =600+900+180050+60+90=3300200=16.5= 600+900+180050+60+90=3300200=16\displaystyle \frac{600 + 900 + 1800}{50 + 60 + 90} = \frac{3300}{200} = 16.5 **Conclusion:** The combined mean is **16.5**. 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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