Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 2914 of 473

The mean annual salary of all employees in a company is $\displaystyle 25,000$ . The mean salary of male and female employees is $\displaystyle 27,000$ and $\displaystyle 17,000$ respectively. Find the percentage of males and females employed by the company.

Options

\displaystyle 60\%

and

\displaystyle 40\%

\displaystyle 70\%

and

\displaystyle 25\%

\displaystyle 70\%

and

\displaystyle 30\%

\displaystyle 80\%

and

\displaystyle 20\%

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Correct Answer

✅ Option d — $\displaystyle 80\%$ and $\displaystyle 20\%$

All Options:

A $\displaystyle 60\%$ and $\displaystyle 40\%$
B $\displaystyle 70\%$ and $\displaystyle 25\%$
C $\displaystyle 70\%$ and $\displaystyle 30\%$
D $\displaystyle 80\%$ and $\displaystyle 20\%$

Detailed Solution & Explanation

**Step 1: Let proportion of males

\displaystyle = p

and females

\displaystyle = (1-p)

.**

27000p + 17000(1-p) = 25000

**Step 2: Solve.**

27000p + 17000 - 17000p = 25000

10000p = 8000

p = 0.8 = 80\%

Females

\displaystyle = 1 - 0.8 = 0.2 = 20\%

. **Note:** The computed percentages are **80% males and 20% females** (Option D). The `correct_option` is A (60% and 40%). Let us verify A:

\displaystyle 27000 \times 0.6 + 17000 \times 0.4 = 16200 + 6800 = 23000 \neq 25000

. Verifying D:

\displaystyle 27000 \times 0.8 + 17000 \times 0.2 = 21600 + 3400 = 25000

✓ 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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The mean annual salary of all employees in a company is 25,000\displaystyle 25,00025,000. The mean salary of male and female employees is 27,000\displaystyle 27,00027,000 and 17,000\displaystyle 17,00017,000 respectively. Find the percentage of males and females employed by the company.