Measures of Central Tendency and DispersionMCQMTP Apr 21Question 2899 of 473
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The mean height of girls in class in 162cm while for boys is 182cm. The ratio of no. of girls: boys is 1:2. Find the mean height of the whole class

Options

A170 cm
B180 cm
C154 cm
D175.33
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Correct Answer

✅ Option d — 175.33

All Options:

  • A170 cm
  • B180 cm
  • C154 cm
  • D175.33

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Detailed Solution & Explanation

**Step 1: Set up variables.** Girls : Boys =1:2\displaystyle = 1 : 2. Let girls =1k\displaystyle = 1k, boys =2k\displaystyle = 2k. **Step 2: Apply combined mean formula.** xˉcombined=1k×162+2k×1821k+2k=162+3643=5263=175.33 cm\bar{x}_{combined} = \frac{1k \times 162 + 2k \times 182}{1k + 2k} = \frac{162 + 364}{3} = \frac{526}{3} = 175.33 \text{ cm} **Note:** The computed mean is **175.33 cm** (Option D), not 154 cm (Option C). The correct answer is 175.33. 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 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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