Measures of Central Tendency and DispersionMCQPYQ June 24 Series IIQuestion 2933 of 473
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The average age of 15 students is 15 years. Out of these the average age of 5 students is 14 years and that of other 9 students is 16 years, then the age of 15th student is ____.

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

✅ Option a — 11 years

All Options:

  • A11 years
  • B14 years
  • C15 years
  • DNone of these

Detailed Solution & Explanation

We are given: - Total number of students: N=15\displaystyle N = 15 - Average age of all 15 students: xˉ=15\displaystyle xˉ=15\displaystyle \bar{x} = 15 years - Sum of ages of all 15 students: Sumtotal=15×15=225\displaystyle Sum\displaystyle \text{Sum}_{total\displaystyle \text{total}} = 15 ×\displaystyle \times 15 = 225 years - Number of students in the first group: n1=5\displaystyle n_1 = 5 - Average age of this group: xˉ1=14\displaystyle xˉ1=14\displaystyle \bar{x}_1 = 14 years - Sum of ages of this group: Sum5=5×14=70\displaystyle Sum5=5\displaystyle \text{Sum}_5 = 5 ×\displaystyle \times 14 = 70 years - Number of students in the second group: n2=9\displaystyle n_2 = 9 - Average age of this group: xˉ2=16\displaystyle xˉ2=16\displaystyle \bar{x}_2 = 16 years - Sum of ages of this group: Sum9=9×16=144\displaystyle Sum9=9\displaystyle \text{Sum}_9 = 9 ×\displaystyle \times 16 = 144 years - Total number of students accounted for: 5+9=14\displaystyle 5 + 9 = 14 students - Combined sum of ages of these 14 students: Sum14=70+144=214\displaystyle Sum14=70+144=214\displaystyle \text{Sum}_{14} = 70 + 144 = 214 years We can find the age of the 15th student by subtracting the sum of the ages of the 14 students from the total sum of the ages of the 15 students: Age15th=Sumtotal−Sum14=225−214=11 yearsAge\displaystyle \text{Age}_{15th\displaystyle \text{th}} = Sum\displaystyle \text{Sum}_{total\displaystyle \text{total}} - Sum14=225−214=11\displaystyle \text{Sum}_{14} = 225 - 214 = 11 years\displaystyle \text{ years} 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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