Central Tendency & DispersionMTP June 22Question 3246 of 473
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The QD from the following observations is 10,18,20,28,15,17,22,25,29,32,34\displaystyle 10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34 is equal to:

Options

A8\displaystyle 8
B6\displaystyle 6
C10\displaystyle 10
D9\displaystyle 9
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Correct Answer

✅ Option b — 6\displaystyle 6

All Options:

  • A8\displaystyle 8
  • B6\displaystyle 6
  • C10\displaystyle 10
  • D9\displaystyle 9

Detailed Solution & Explanation

We are given the observations: 10,18,20,28,15,17,22,25,29,32,34\displaystyle 10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34. The number of observations is n=11\displaystyle n = 11. 1. Arrange the data in ascending order: 10,15,17,18,20,22,25,28,29,32,3410, 15, 17, 18, 20, 22, 25, 28, 29, 32, 34 2. Find the first quartile (Q1\displaystyle Q_1): - Position of Q1=n+14=11+14=3rd\displaystyle Q_1 = \frac{n+1}{4} = \frac{11+1}{4} = 3^{\text{rd}} term. - Q1=17\displaystyle Q_1 = 17. 3. Find the third quartile (Q3\displaystyle Q_3): - Position of Q3=3(n+1)4=3(11+1)4=9th\displaystyle Q_3 = \frac{3(n+1)}{4} = \frac{3(11+1)}{4} = 9^{\text{th}} term. - Q3=29\displaystyle Q_3 = 29. 4. Calculate Quartile Deviation (Q.D.): Q.D.=Q3−Q12=29−172=6\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{29 - 17}{2} = 6 Hence, **Option B** is the correct answer.

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