Measures of Central Tendency and DispersionMCQMTP Nov 18Question 2879 of 473
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The mean salary for a group of for a group of 50 male workers is Rs.4800 per month and that for a group of 50 female workers is Rs. 5600. the combined mean salary is

Options

A5100
B5200
C5300
D5400
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Correct Answer

✅ Option b — 5200

All Options:

  • A5100
  • B5200
  • C5300
  • D5400

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Detailed Solution & Explanation

**Step 1: Identify the given data.** nm=50\displaystyle n_m = 50, xˉm=4800\displaystyle \bar{x}_m = 4800 (males); nf=50\displaystyle n_f = 50, xˉf=5600\displaystyle \bar{x}_f = 5600 (females). **Step 2: Apply combined mean formula.** xˉcombined=nmxˉm+nfxˉfnm+nf=50×4800+50×560050+50\bar{x}_{combined} = \frac{n_m \bar{x}_m + n_f \bar{x}_f}{n_m + n_f} = \frac{50 \times 4800 + 50 \times 5600}{50 + 50} =240000+280000100=520000100=5200= \frac{240000 + 280000}{100} = \frac{520000}{100} = 5200 **Note:** The computed answer is **5200** (Option B), not 5100 (Option A). Since both groups have equal size (50 each), the combined mean is simply 4800+56002=5200\displaystyle \frac{4800+5600}{2} = 5200. 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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