Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 2860 of 473
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If the mean of the following distribution is 6, then the value of P\displaystyle P is X | 2 | 4 | 6 | 10 | P+5 F | 3 | 2 | 3 | 1 | 2

Options

A7\displaystyle 7
B8\displaystyle 8
C9\displaystyle 9
D11\displaystyle 11
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Correct Answer

✅ Option a — 7\displaystyle 7

All Options:

  • A7\displaystyle 7
  • B8\displaystyle 8
  • C9\displaystyle 9
  • D11\displaystyle 11

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Detailed Solution & Explanation

**Step 1: Set up the frequency table.** | X\displaystyle X | f\displaystyle f | fX\displaystyle fX | |-----|-----|------| | 2 | 3 | 6 | | 4 | 2 | 8 | | 6 | 3 | 18 | | 10 | 1 | 10 | | P+5\displaystyle P+5 | 2 | 2(P+5)\displaystyle 2(P+5) | **Step 2: Apply the mean formula.** Xˉ=∑fX∑f\bar{X} = \frac{\sum fX}{\sum f} ∑f=3+2+3+1+2=11\sum f = 3 + 2 + 3 + 1 + 2 = 11 ∑fX=6+8+18+10+2(P+5)=42+2P+10=52+2P\sum fX = 6 + 8 + 18 + 10 + 2(P+5) = 42 + 2P + 10 = 52 + 2P **Step 3: Substitute mean = 6.** 6=52+2P116 = \frac{52 + 2P}{11} 66=52+2P66 = 52 + 2P 2P=14  ⟹  P=72P = 14 \implies P = 7 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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