Central Tendency & DispersionMTP Nov 19Question 2971 of 473
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The third decile for the numbers 15,10,20,25,18,11,9,12\displaystyle 15, 10, 20, 25, 18, 11, 9, 12 is

Options

A13\displaystyle 13
B10.70\displaystyle 10.70
C11\displaystyle 11
D11.50\displaystyle 11.50
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Correct Answer

✅ Option b — 10.70\displaystyle 10.70

All Options:

  • A13\displaystyle 13
  • B10.70\displaystyle 10.70
  • C11\displaystyle 11
  • D11.50\displaystyle 11.50

Detailed Solution & Explanation

To find the 3rd\displaystyle 3^{\text{rd}} decile (D3\displaystyle D_3) for the observations: 15,10,20,25,18,11,9,12\displaystyle 15, 10, 20, 25, 18, 11, 9, 12: 1. Arrange the data in ascending order: 9,10,11,12,15,18,20,259, 10, 11, 12, 15, 18, 20, 25 Here, the number of observations is n=8\displaystyle n = 8. 2. The position of D3\displaystyle D_3 is given by: Position of D3=3(n+1)10=3(8+1)10=2710=2.7th term\text{Position of } D_3 = \frac{3(n+1)}{10} = \frac{3(8+1)}{10} = \frac{27}{10} = 2.7^{\text{th}} \text{ term} 3. Calculate the value of the 2.7th\displaystyle 2.7^{\text{th}} term: D3=2nd term+0.7×(3rd term−2nd term)D_3 = 2^{\text{nd}} \text{ term} + 0.7 \times (3^{\text{rd}} \text{ term} - 2^{\text{nd}} \text{ term}) D3=10+0.7×(11−10)=10+0.7×1=10.70D_3 = 10 + 0.7 \times (11 - 10) = 10 + 0.7 \times 1 = 10.70 Hence, **Option B** is the correct answer.

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