Central Tendency & DispersionPYQ 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

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.

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