Central Tendency & DispersionMTP Nov 21Question 2977 of 473
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Find D6\displaystyle D_6 for the following observations. 7,9,5,4,10,15,14,18,6,20\displaystyle 7, 9, 5, 4, 10, 15, 14, 18, 6, 20

Options

A11.40\displaystyle 11.40
B12.40\displaystyle 12.40
C13.40\displaystyle 13.40
D13.80\displaystyle 13.80
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Correct Answer

✅ Option b — 12.40\displaystyle 12.40

All Options:

  • A11.40\displaystyle 11.40
  • B12.40\displaystyle 12.40
  • C13.40\displaystyle 13.40
  • D13.80\displaystyle 13.80

Detailed Solution & Explanation

To find the 6th\displaystyle 6^{\text{th}} decile (D6\displaystyle D_6) for the observations: 7,9,5,4,10,15,14,18,6,20\displaystyle 7, 9, 5, 4, 10, 15, 14, 18, 6, 20: 1. Arrange the data in ascending order: 4,5,6,7,9,10,14,15,18,204, 5, 6, 7, 9, 10, 14, 15, 18, 20 Here, the number of observations is n=10\displaystyle n = 10. 2. The position of D6\displaystyle D_6 is given by: Position of D6=6(n+1)10=6(10+1)10=6610=6.6th term\text{Position of } D_6 = \frac{6(n+1)}{10} = \frac{6(10+1)}{10} = \frac{66}{10} = 6.6^{\text{th}} \text{ term} 3. Calculate the value of the 6.6th\displaystyle 6.6^{\text{th}} term: D6=6th term+0.6×(7th term−6th term)D_6 = 6^{\text{th}} \text{ term} + 0.6 \times (7^{\text{th}} \text{ term} - 6^{\text{th}} \text{ term}) D6=10+0.6×(14−10)=10+0.6×4=10+2.4=12.4D_6 = 10 + 0.6 \times (14 - 10) = 10 + 0.6 \times 4 = 10 + 2.4 = 12.4 Since 12.40\displaystyle 12.40 is the mathematically correct value, and Option B is closest or represents the correct choice (noting textbook key discrepancies that may list Option B), we select Option B. Hence, **Option B** is the correct answer.

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