Measures of Central Tendency and DispersionMCQPYQ June 24 Series IIQuestion 2934 of 473
All Questions

The average of marks obtained by 120 students in a certain examination is 35. If the average marks of passed students is 39 and that of the failed students is 15, what is the number of students who passed in the examination?

Options

A100
B150
C200
DNone of these
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Correct Answer

✅ Option a — 100

All Options:

  • A100
  • B150
  • C200
  • DNone of these

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Detailed Solution & Explanation

Let n1\displaystyle n_1 be the number of passed students and n2\displaystyle n_2 be the number of failed students. - Total number of students: N=n1+n2=120  ⟹  n2=120−n1\displaystyle N = n_1 + n_2 = 120 \implies n_2 = 120 - n_1 - Average marks of all 120 students: xˉ=35\displaystyle \bar{x} = 35 - Average marks of passed students: xˉ1=39\displaystyle \bar{x}_1 = 39 - Average marks of failed students: xˉ2=15\displaystyle \bar{x}_2 = 15 Using the formula for the combined mean: xˉ=n1xˉ1+n2xˉ2n1+n2\bar{x} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2} Substitute the given values: 35=39n1+15(120−n1)12035 = \frac{39 n_1 + 15(120 - n_1)}{120} Multiply both sides by 120: 4200=39n1+1800−15n14200 = 39 n_1 + 1800 - 15 n_1 4200−1800=24n14200 - 1800 = 24 n_1 2400=24n12400 = 24 n_1 n1=100n_1 = 100 Thus, the number of students who passed in the examination is 100. 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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