Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 2928 of 473
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The average age of a group of $10$ students was $20$ years. The average age is increased by two years when two new students joined the group. What is the average age of two new students who joined the group ?

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

✅ Option d — $32$ years

All Options:

  • A$22$ years
  • B$30$ years
  • C$44$ years
  • D$32$ years

Detailed Solution & Explanation

**Step 1: Total age of original 10 students.** Total10=10×20=200 yearsTotal10=10\displaystyle \text{Total}_{10} = 10 ×\displaystyle \times 20 = 200  years\displaystyle \text{ years} **Step 2: New total after 2 new students join.** New number of students =10+2=12\displaystyle = 10 + 2 = 12. New average =20+2=22\displaystyle = 20 + 2 = 22 years. New total=12×22=264 yearsNew total=12\displaystyle \text{New total} = 12 ×\displaystyle \times 22 = 264  years\displaystyle \text{ years} **Step 3: Sum of ages of 2 new students.** Sum of 2 new=264−200=64 yearsSum of 2 new=264−200=64\displaystyle \text{Sum of 2 new} = 264 - 200 = 64  years\displaystyle \text{ years} **Step 4: Average age of 2 new students.** Average=642=32 yearsAverage=642=32\displaystyle \text{Average} = \frac{64}{2} = 32  years\displaystyle \text{ years} **Note:** The computed average is **32 years** (Option D), not 44 years (Option C). 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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