The mean salary for a group of 40 female workers is 5200 per month and that for a group of 60 male workers is 6800 per month. What is the combined salary ?

Option a: 6160. Solution: Step 1: Apply combined mean formula. xcombined = xf + nm xmnf + nm = 40 × 5200 + 60 × 6800/40 + 60 = 208000 + 408000/100 = 616000/100 = 6160 Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IQuestion 2931 of 473

All Questions

The mean salary for a group of $\displaystyle 40$ female workers is $\displaystyle 5200$ per month and that for a group of $\displaystyle 60$ male workers is $\displaystyle 6800$ per month. What is the combined salary ?

Options

\displaystyle 6160

\displaystyle 6280

\displaystyle 6890

\displaystyle 6920

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Correct Answer

✅ Option a — $\displaystyle 6160$

All Options:

A $\displaystyle 6160$
B $\displaystyle 6280$
C $\displaystyle 6890$
D $\displaystyle 6920$

Detailed Solution & Explanation

**Step 1: Apply combined mean formula.**

\bar{x}_{combined} = \frac{n_f \bar{x}_f + n_m \bar{x}_m}{n_f + n_m}

= \frac{40 \times 5200 + 60 \times 6800}{40 + 60} = \frac{208000 + 408000}{100} = \frac{616000}{100} = 6160

Hence, **Option A** 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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The mean salary for a group of 40\displaystyle 4040 female workers is 5200\displaystyle 52005200 per month and that for a group of 60\displaystyle 6060 male workers is 6800\displaystyle 68006800 per month. What is the combined salary ?