Central Tendency & DispersionMTP June 24 Series IIQuestion 2988 of 473
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Find Q1\displaystyle Q_1 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

A4.75\displaystyle 4.75
B5.25\displaystyle 5.25
C5.75\displaystyle 5.75
D6.25\displaystyle 6.25
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Correct Answer

✅ Option c — 5.75\displaystyle 5.75

All Options:

  • A4.75\displaystyle 4.75
  • B5.25\displaystyle 5.25
  • C5.75\displaystyle 5.75
  • D6.25\displaystyle 6.25

Detailed Solution & Explanation

To find the first quartile (Q1\displaystyle Q_1) 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 Q1\displaystyle Q_1 is given by: Position of Q1=n+14=10+14=2.75th observation\text{Position of } Q_1 = \frac{n+1}{4} = \frac{10+1}{4} = 2.75^{\text{th}} \text{ observation} 3. Calculate the value of the 2.75th\displaystyle 2.75^{\text{th}} observation: Q1=2nd observation+0.75×(3rd observation−2nd observation)Q_1 = 2^{\text{nd}} \text{ observation} + 0.75 \times (3^{\text{rd}} \text{ observation} - 2^{\text{nd}} \text{ observation}) Q1=5+0.75×(6−5)=5+0.75×1=5.75Q_1 = 5 + 0.75 \times (6 - 5) = 5 + 0.75 \times 1 = 5.75 Hence, **Option C** is the correct answer.

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